This is just very, very basic stuff, if you have already played a bit of tf2, move on.

Damage dropoff.
The way tf2 works, the further you are from your enemy the less damage you do. So hitting someone right across the map will only hurt them a little and hitting the guy right next to you will hurt them a lot. This makes TF2 a game about closing with the enemy/not letting the enemy close with you. The only things drop off doesn't apply to are crits, including sniper head shots and sentry bullets. Sentry rockets will actually do more damage the closer you (not your sentry) is to the guy it is shooting at. The medics crossbow actually has reverse drop off, the further away you are, the more damage, though you will seldom get hit by one.

Med ubercharge rate.
Charge rate works like this: Hurt player>overhealed player>player on dispenser or cart/being healed by another med. So if a med is healing you, do the nice thing for him and stay away from a dispenser unless things are getting hot. Similarly for standing on the cart, if there are already 5 guys pushing it. Step off if you are really hurt and give the med someone to charge at full speed on. Another part of this is called grinding, if you have a med on you who is getting close to uber, or you have to have that uber to get through the next choke, you hurt yourself so the med gets his charge faster. (engi cant do this in 99% of circumstances, its more for sollis/demos). The correct way to grind is never to fire off all your shots so you have to reload fully, keep a few spare to fight off people who come annoy you.
Grinding doesn't work during setup time.
If you are playing med and there is only a med and the guy he is healing near you, heal the med, you will both charge faster.

Spy checking
Spies can disguise as members of the opposing team. You can still shoot and kill them and if you walk into them you will 'bump' them rather than going right through like your other teammates.
Shoot at everybody you see and if you find a spy, work hard on killing him.
If you see a teammate run round a corner from where you know there are nothing but enemies, its probably a spy. If you 'bump' into something while walking somewhere, its a spy. A teammate running in the opposite direction to everybody else, often right at your sentries, spy. If you shoot at someone to spycheck them and they try to move out of your way rather than just running through you, spy. If you see a friendly scout and when you press Tab you have no scouts, spy. If you see an engi frantically trying to unsap his stuff while another player runs around sapping it, PROTIP: THE OTHER PLAYER IS A SPY. SHOOT THE ♥♥♥♥♥♥, DONT JUST WATCH.
New players especially are obvious spy bait, watch your back, check everybody and if you get onto an enemy spy, do your damndest to kill him.

Stay at full health
Most good players play from healing source to healing source. If you have the option always be at full health

If a med is present, the health packs all belong to the MEDIC
Ill say later the med is the most powerful class in the game, apart from basic healing you have ubers and kritzes and the ability to buff all players up to 150% health. If you are playing a class other than med, the med is more important than you. Throwing your life away to save a medic is often smart team play. If you and a medic are both hurt near a health pack, he can heal you, LET THE MED TAKE THE HEALTHPACK. If you are only a little hurt/fairly safe and a med is healing you, don't even go for health packs, leave them incase the med needs them later.

First, lets talk weapons, loadouts and general stuff for hurting people.

Primaries

The standard Shottie.

The shottie is a secondary for most classes, but a primary for the engi, remember this, it is quite capable of killing most enemies in a few shots, but don't go trying to front on a soldier or the like and think you will win out. That said, the shottie is a very respectable weapon, if you can hit stuff from close up a few times, expect it to die, one of the big differences between a good engi and a great one is shotgun accuracy, learn to line up your shots and hit things solidly to give yourself a better chance in close range fights.

The Frontier Justice.

This gun is why you want spot on shotgun accuracy, 3 shots isn't much, if you miss twice, expect to be dead in a close range fight. Revenge crits though, are sweet, oh so sweet. Generally you want to use the justice with the gunslinger, but if you have a sentry with 3 or more kills, don't be afraid to go back to spawn and switch out. The justice can 1 shot many classes and seriously hurt most others and having 10 revenge crits up the pipe can make you a serious threat. Also don't underestimate how scary that crit sound is, if you are in trouble, hitting someone with a crit from a distance will often make them think twice.

The Pomson.

Interesting gun, perfect accuracy, fun effects on spies and medics as well, but lower close in damage and clip size. Pomson is my weapon of choice for annoying dead ringer spies, hitting medics is good and will often make them think twice about being in your view range but don't count on it saving your life. When wielding the pomson, don't be afraid to spam out a lot of shots at everything and nothing, its a good gun for annoying people, hitting snipers at long range, etc but its low close in damage output makes a shottie generally a better choice for me.

The Widowmaker.

Uses metal to fire, has no clip. Again, interesting gun and can be hilarious for things like kritzes and buff banners but you want fantastic accuracy for it to be really useful, I find it very easy to end up with no metal using this gun, which usually means im about to die. Shooting buildings is a great way to build up your metal though, so if the enemy is using minisentries it can be a workable choice. My play style often leaves me scavenging for metal though, so id rather a standard shottie generally. In the right hands it can be a wrecking machine, but those aren't my hands.

The Rescue ranger.

Idea is interesting, be able to grab buildings from far away, so the best use of it is to be at a forward attacking position, grab a sentry from far away and drop it in. Problem here is your sentry needs to be in full view of that attacking position for the whole time you are making your way there. Fair chance your sentry is going to get taken down and you are going to be left with a low powered gun and that's the rangers other problem, like the pomson, its not a good killing gun, you can get kills with it, but the shottie is generally better.
I've used the ranger well a few times, generally you want a good plan and a lot of luck, but a real smart war guy once said 'No plan survives contact with the enemy' and I agree.
Its a fun gun, not a good gun imo.


Secondaries

The Pistol.

Ohhh my sweet baby, I strokes it, I loves it, I croons to it at night. Farking love the pistol. If im running Frontier justice, the pistol is my primary weapon, save those revenge crits for when they are needed. You are never going to run out of ammo for the pistol, its got good accuracy at range, great rate of fire and reload speed. Unless you are being ninja, shoot at everybody you can see with the pistol, there is just no reason not to. Its surprisingly good against buildings as well, ive taken out many a sentry with my little pistol. Does ok damage at close range just remember that most classes have a 'bang you are dead' gun, the pistol is going to take time to kill at any range.

The Wrangler.

I play engi in Highlander and the wrangler is pretty much essential kit there, not so much in normal play. If you want to turtle, the wrangler is a good choice, I generally don't turtle. Support is the big thing with the wrangler, if you have other players around looking after you (pyro with good reflect skill and homewrecker by choice) the wrangler can be a game winner. Also great for burning up enemy ubers, it often takes a full uber to kill a wrangled sentry, then the rest of the team can come in and mop up, don't shoot at the uber, clean up any other classes that push in with it. My biggest issue with the wrangler is it ties you to your sentry and I like to be very mobile as an engi. Wrangled minis can also be great against snipers, enemy buildings etc, its a perfectly accurate but low damage gun, use it right and it can be great.
Generally for pub play for me though pistol>wrangler.

The Short circuit.

Idea is good, reality not so good. The only time ive seen the circuit used well is with a few engis together turtled up, 2 with wranglers, 1 with circuit doing little but busting stickies and rockets. Other than that, its just not useful. I don't like to turtle, so I pretty much never use it.


Melee

Building info in the building section.

Standard wrench.

Hit stuff with it a few times and it will die, if crits are enabled, often just hit stuff once and it will die. Bog standard melee stuff really. Totally respectable as a weapon, good against demos and spies especially.

The Jag.

Faster build, lower damage. Its a good tradeoff, that said in melee it feels a bit like a wiffleball bat. if you are running the jag, you want to be using the shottie up close

Southern Hospitality.

Bleed damage, Fire vulnerability, no crits. Bleed damage is good, nothing says 'run away and get a health pack' like having your health constantly eaten. Makes pyros, especially flaregunners a huge threat though, I don't use it for this reason. If crits are on, the standard wrench will usually have higher DPS, without any penalties. Normally if im in a melee fight, I don't stop clubbing till someone is dead, having the enemy run off bleeding isn't part of the plan. If crits are off and the enemy has no decent pyros, ok, but its not something I ever use.

Eureka effect.

Tele to spawn, no building move. Idea I believe, is that there is full metal in spawn. Problem is, there is generally metal all over the damn place and I can usually get metal in the time it takes to tele to spawn, without even considering the time it takes you to walk back. And you cant move your damn buildings. In a word. Ick. Its a silly toy, nothing else.

Gunslinger.

Extra health, 3 punch combo, MINISENTRIES! Ill talk about sentries in the next section, so for now, extra health is great, will up your survivability markedly, 3 punch combo isn't easy to do, but can be a killer against stuff like heavies that aren't paying attention and sollis.

Little note, I have strange Jag, gunslinger and Standard wrench. My sentry kill to melee kill ratios for each are about: 1:6 gunslinger, 1:10 wrench, 1:20 jag. Usually running gunslinger with the frontier and the extra health means more melee time, the jag is really low powered as a melee weapon.

Standard Sentries

Meat and potatoes right here. They shoot stuff, that is all. Im going to go into a lot more detail in the tactics section, so some general stuff now.
Upgrading from one lvl to another takes about 10 seconds if the sentry doesn't shoot, this is important. This is a damn long time ingame so be smart with your sentries, generally for my mobile and aggressive play style I find a lvl 2 will do anything a lvl 3 can with a smaller profile, hitbox and faster build time after a move. I like to build sentries on big metal packs/dispensers, upgrade to lvl 2 then run them where I want them. Dumping a lvl 1 in the middle of a battlefield just to make people waste shots that may be otherwise intended for you is a decent tactic as well.
General wisdom is Big sentry = defence, minis = attack, however dropping a big sentry on the edge of a cap point during an attack can be a game winner on blue, also if I can build in setup time, im pretty much always running a big sentry for my first life on blue.

Oh, and if it dies, it dies, its pretty much never worth killing yourself to save a sentry, if things are too ugly then save yourself and let the sentry buy you some time.

Dispensers

Potential game winners. Your dispenser placement will often dictate where the front lines are, people will move back and forth from it and that area will be a lynchpin of your defence. So having your dispenser too far back will often let the enemy take territory that could have been at least contested. Don't be stupid with your dispenser placement, they want to be as far forward as possible, but out of direct line of fire, around corners, hidden behind piles of stuff, whatever. Use your damn head. If things aren't totally frantic, upgrading your dispenser to lvl 3 should be a priority. Placing your dispenser and running off to do other things while it builds up some metal so you can upgrade it to full in one sitting is often a good idea as well.
Oh, and engi 101 states your sentries cant shoot through your dispensers, so don't build them near each other, unless you are king turtle man, the dispenser will do more good for the team where it is accessible for healing than stuck behind you and your sentry off in some corner.

Minisentries

They are small, they are cheap and they are annoying as hell. Drop minisentries in every corner, nook, cranny, on every roof, in every valley. Make your enemies live in fear of that damn tickticktickticktick as they ping away at their health. Your placement doesn't have to be smart, just throw them out, the enemy will be looking for threats from smart places, its the random 'WTF IS THAT DOING THERE?!' that drives them crazy.
The road to engi greatness is paved with the remains of fallen minisentries, never care if they die, if you are being attacked, just dump them as you run, make your enemies waste shots on them while you bolt off on another adventure. You never want to die with 100+ metal when you are running minis, as you go down, there should be another damn minisentry going up, just so your enemies know that this is never going to end. Again, more in the tactics section.

Teleporters

Another game winner in an obvious way, tele stuff is fairly obvious so ill avoid the simple stuff.
Teles can be used to force your team to be aggressive, if the exit gives no option but to attack then that is what your players are going to do, if you feel your team is playing to defensively/acting like damn cowards having a tele that gives no other option but attacks on enemy strongpoints can be a solution. It can also get a lot of players killed, but war is hell and they will either be stronger for the experience or go back to playing COD.
Teles also aren't useless in stuff like last cap defences where there is nowhere to tele to. If your dispenser and sentry are looking good, throw your teles out (both of them) right in the middle of the battlefield, this gives nubs and spies something to attack that isn't you, your teammates or your sentry. I find it rather funny to watch and uber run out to attack then have the whole thing get wasted as they get distracted like kittens with shinies by teles that obviously go nowhere.

General Movement:

Run, jump, be unpredictable, blah blah blah. That's general stuff, you can work it out.

Rocket jumping, now we are talking. Smart play for sollis/sticky demos is 'shoot feet, get kill' do the obvious thing and crouch jump when this happens to launch you, hopefully where you want to go, either the hell away, or especially in the case of demos, right into their faces. Demos super powerful AOE attacks are more of a liability when they have an angry flying engi attempting to club their faces in. You might die, but they definitely will, do this a few times and they should start to fear you a bit. This is where im going to get a bit mumbo jumbo but stick with it, this is the core of my playstyle.

Psychology in TF2

Now this stuff often wont apply to great players and its pretty much useless in highlander, but for 90% of pub play its damn useful to at least think about it.

Repetition, or kick the dog till it learns, then learn from it.
If you can repeatedly do like I said in the top paragraph and jump into a demos face and club him down with your wrench, he is going to find something else to do rather than engage you in those circumstances over and over. If every time the heavy comes up against you, you just hammer him down with the frontier justice, he will try and avoid you. If every time an enemy explosive jumps, he gets splattered against the skybox by a wrangler/frontier justice shot, they will cut out all that silly jumping. It sounds a bit pie in the sky, but once you have hammered the same person multiple times in the same way, you can probably expect to be safe from that sort of attack/attack from that direction for a while. Totally expect them to attack, however from another angle/loadout option. Be aware of what you do to who and how that will probably change their actions. Simple stuff like if an enemy has been killed by a sentry a few times, move the sentry/yourself so you covers the place where he is going to attack your initial sentry position from. Gamesense grasshopper, gamesense.

FEAR ME FOR I AM BATTLE ENGI!
Most players (rightly) view the engi as a low powered combat class, this means the often don't expect to be oneshotted by a frontier justice, walk around with your pistol out to make yourself look weak and harmless, then ambush at a corner.
The other side of this is what I call the rabid hamster. You run a balls out attack from the flank/behind a pile of enemy players, if you can take a few out in the initial confusion, keep the attack up, preferably from point blank range. A majority of players will try and run away from the crazed nutter engi and backs make better targets than fronts, even if you are only hammering at them with your pistol by now.
The trick here is what people see. An engi is generally a low risk target, a heavy, a high risk one. If you blow away the heavy standing next to a player with a frontier/surprise melee attack, that guy is going to see you as a higher risk, even if you are now holding an unloaded gun.
You notice this most if you are really dominating a server, many enemies will just try and stay away from you, its just not worth trying to engage that nutter engi.
Again, its a bit mumbo jumbo, but make them scared, make them run, shoot them in the back is a good strat.

Way of the ninja, or not getting shot at for winners.
So you want to be a cheeky bastard, you want teles behind enemy spawns, sentries where there shouldn't be sentries and generally to make a jerk out of yourself. Good for you son, here we go. Step 1 of breaking through enemy lines, is to get through enemy lines, strangely enough. 1st off, there are some maps where this is near to impossible, there is just too much open ground, chokes etc. But to hell with that.
First thing id suggest is not shooting at people. It makes them angry, makes them chase you and generally puts a spanner in the works. If given the choice of the solli shooting rockets at them and then engi ducking off to the side, most people will engage the solli and leave you to wander on your merry way, looking directly at an enemy as they look at you can have a similar effect, strangely enough, if there are other people shooting at them ive often been able to just walk past players by just walking past with my pistol out, not looking anywhere but directly ahead.
Second to not shooting, is not being shot at. Way most tf2 is played, if someone starts shooting at you, they are going to keep going till you are dead. So kill them. Really the only option at this point, if they aren't alone, running and shooting is probably the best option, if you are already through the lines, then an ambush and then getting the hell out of there (always expect someone to have informed their team if an engi kills them behind the lines).
Be very aware of where the other team is going to look as you get close/go past highly trafficked areas. If you are well behind the lines pretty much everybody is going to be taking the shortest route, turning left at spawn, jumping over this ledge, walking down corridor A. As a ninja you want to be walking down corridor B, crouching past the ledge (people pretty much never look down) and hiding to the right of their spawn, and again not shooting at people. Your goal is to get a tele out the back in an out of the way place not shoot pyros in the back, THEN you can build cheeky sentries and get taunt kills at their spawn, shoot pyros in the back, etc.

The early break out.

The Majority of the times im getting through the lines its actually in my first life right after setup time. Badwater especially im notorious for this and im probably about 70% successful getting through to red spawn as blue on badwater. Right after setup time ALL the enemy focus is right at the gates, if you can just break through that, you are pretty much home free. Other maps its a bit more difficult, but badwater has that nice long tunnel that runs all the way through the first section. If you get to that, you are about 50% of the way there, nobody is expecting someone to actually walk all the way to red spawn right off the bat. Generally right after setup time is the most intense part of any fight, you will have multiple ubers flying around and a very thin line to get through, its a perfect time to try and break out.

A few general tactics I use that I find work well, general gameplay tidbits really.

Fail to plan is planning to fail.

This mostly applies to playing defence on pl maps, a bit more on 5 points and the like. Blue is pretty much always going to get to the first point, expect this and be ready, when things are starting to turn, you want to have your dispenser/teles ready for the next hold unless you are trying to do something cheeky. As an example, first stage goldrush defence, unless things are going super well, im putting up a dispenser in preparation for holding second stage on my first or second death. Just dump it in a good spot and keep going, when you actually come back to defend, it will be nice and full of metal and ready for you. Last stage goldrush defence, I always build a tele at what becomes your spawn door after first cap during setup time. When blue gets serious about getting first cap, I run back and set up a tele near second cap then usually upgrade it. This means by the time blue gets to second we are in a position to hold rather than just hoping people will be able to waddle their fat butts from spawn to there without being distracted by shinies or killed by spies.
5 points are similar, nothing wrong with having a decent tele set up to so you can quickly get players in to the point behind the one you are holding now if things go pearshaped.

If its not shiny, its not worth shooting

Simple little thing for teles. If they aren't active, they are a lot harder to see/hear and people are less likely to smash them. This is good for leaving a tele someweres that will be out of the way once the fight moves past it, but is very forward right now. It can be better to not build your entrance and get that tele exit stashed away, then once the enemy has capped/fight has moved past etc, you get your entrance set up and tele in behind them.

Level 2 will do

Most engi buildings aren't all that good at lvl 1, there are spots to do it, but not many. It takes a long time to get things up to lvl 3. Half way is the obvious compromise. Lvl 2 tele is twice as fast as a lvl 1, that's a huge upgrade, on a smaller server (<20) unless ive got spare time to be upgrading it, lvl 2 tele is fine for me. With a DPS of 128 a lvl 2 sentry can kill most classes in <1.5 seconds. If you place it smart, that's .5 seconds for them to work out what's going on, .5 seconds to find and aim at the sentry then only another .5 of a second to maybe get a shot off. Once they have died once to it, its a different story. I generally expect a sneaky sentry to get no more than 3 kills before it goes down. People are aware of where it is by then. However for the 10/15 seconds it took me to build a lvl 2, id call that worth it. Lvl 3, you are looking at 20/30 seconds depending on circumstances and that's just too long to stand in one spot doing stuff all for the modern go go engi.

A time for the little guys, when to use lvl 1s.

The dump and run sentry is the most obvious, If you have to get down to the cart/point and start fighting, there is no reason not to dump a sentry on the way. In the heat of a serious push, it can be easy for the other team to overlook the lvl 1 slowly going up in the corner, they also come in very low on the threat scale, so again, they can be overlooked even when they are shooting.
Minis are generally better for this, but if you are ninjaing your way behind the lines, dumping a lvl 1 off to the side/up high as a distraction never hurts, once it starts shooting, people will be looking at it, not at you, even if it doesn't get any kills.
If you have been totally ninja and managed to get a tele up over last point before first is capped or something like that, you want to leave it at lvl 1. Having your whole team trying to camp spawn while the entire other team is out pushing/defending last is a great way to loose a game.

You are the greatest. Making the other useless meatsacks on your team take your tele.

If you are reading this guide hopefully you will already be setting up your teles either nice and forward or just balls out aggressively and NOT doing stuff like setting up all your stuff over second point when everybody else is defending 1st and playing with your wrench/setting up 1/4 of the way into the map when you are trying to push last.
Ergo, your tele is the best and you want to get the maximum amount of said meatsacks through it as quickly as possible. Its a small thing but placing your tele about a 1/2m in front of your spawn door and dead centre is the optimum place. People generally walk out the spawn door and look down at a 45 degree angle, this is where you want your tele. Too close to the door and they will walk over it, too far and they will go for a closer one. If you have multiple spawn doors, either set it up on the one everyone walks out of, or so they have to walk past it if they come out of the back spawn.

Ambush, flank, flank and Ambush again.

Engi is a low health and low damage class compared to all the other classes in TF2. Given the choice you don't want to be taking anything on front on at close range. Mid/long range, throw out some pistol spam for sure, but close range the only way you don't want to be fighting is face to face. If you are initiating the fight you want it on your terms, in the back, in the flank or dropping down onto them from above.
That said, things will often go wrong, when they do, start hammering with your shottie and try to do as much damage as you can before you go down, be careful lining up your shots, you can always get lucky.

The right way to build a sentry.

Again, something simple but worth mentioning. Unless you are standing on a full metal pack or at a dispenser when you build a sentry, get it up to lvl 1, then hit it twice more to get a bit of metal towards the next upgrade. This way if your sentry takes damage or shoots at someone while you are away, you can still get it up to lvl 2 in one hit when you come back with 200 metal. Damn annoying to have to make a second trip out to get more metal cause the sentry has fired 1 shot and you are at 199/200 on the upgrade.

Miniturtle

Now ive said before I don't like to turtle and Im happy to let sentries die, there are a few exceptions though. What I do here is crouch down behind a sentry, (lvl 2 for pref) placed in a very aggressive spot with full metal. Places like right in front of spawns, during the very start of the game, things where you know you are going to be getting allot of players coming at you.
Now most classes (demo excluded) cant actually kill a sentry 1v1 if the engi is behind it and only repairing the damage done. Don't just hold the wrench button down, wait for damage, repair, wait for damage, repair, you don't want to waste metal or a mistimed wrench swing on an upgrade you don't want or filling up ammo when the sentry is under direct attack. Ubered sollis are great for doing this to. Every time a rocket hits, you fix the damage, they cant actually put out enough damage to kill the sentry if you are on your game. If its obvious the sentry is going to go down, get the hell out, preferably early enough that you can get away while everybody is shooting your sentry. Other than that though, hang tough, keep your cool and don't pull out till you are going to run out of metal. In a perfect world, you pull out with you empty of metal and the sentry on full health hammering away. Again, don't shoot while running away unless you think you can get an easy kill. Sentry shooting at me: high threat, shoot back. Running engi: low threat, ignore.

I AM A WOLFPACK OF 2!

Its a simple ambush strat, but allot of people don't do it/aren't ready for it.
You have your sentry set up, people are going to usually attack it from point X. Demos will shoot at if from over this hill, people will corner it from here, etc. Set yourself up to ambush point X with your shotgun. Demos especially like to stop on a point and lob stickies at sentries, hit them from behind/flank from point blank.
Minisentries/frontier combo is great for this. When the minisentry starts shooting, people look at it, wait for 1/2 a second to be sure they have engaged it, they dash out from hiding to shoot them in the back. This is probably the best way ive found of camping a spawn as an engi, drop your mini on the right, hide on the left, they attack the mini, you dash out and kill them, use the pistol to up the chance of the mini killing them, then bank the justice crits, build a sentry on left, hide on the right, etc.

Staring at a wall for winners.

Another simple thing, if you are going to put out a sneaky sentry, don't have it so it is looking right at where people will be walking out of, point it at the wall so people will be right out of cover before it starts shooting. Obviously this only applies if you place the sentry somewheres people wont be looking when they walk past.

Its a team game, innit? Here are some friendly people you will meet while playing TF2.

Stand on your dispenser and shoot heavy.
A heavy standing on a lvl 3 dispenser can tank a lot of damage and fire off as many bullets as he wants. I don't understand people who are happy to do this, but they exist. If you meet this guy, make sure you have your dispenser somewhere he isn't going to get sniped but still has a nice field of view to shoot at stuff in.

Engis best friend, the guard dog pyro
Generally a player who has gotten ♥♥♥♥♥♥ with spies, he goes pyro and does nothing but defend sentry positions. Often on highlander you will have a pyro doing this, equipped with the homewrecker and some pro reflect skills, the pyro/engi combo can make any defensive position a seriously tough nut to crack. Make sure he has a nice dispenser somewhere very nearby and safe. If/when it comes to combat, hang behind the pyro and back him up with pistol and shottie fire. If you have a mic, call threats/spies for your pyro.

Mr/Mrs putsstickiesonsentry Demo

You don't see the Scottish resistance demo often, but when you do, many like to put sticky traps on sentry/dispensers to kill spies. If you have a mic, call when you want the stickies popped.

Yin to my Yang: the backline engi

Personal favourite. If there is a backline engi, I don't have to feel bad about not doing that crap. If he has decent tele setups, I can make hyper aggressive ones that will only last a short time without it costing the team. Ditto for sentries, if someone else has the standard spots covered, mine can easily go somewhere much more fun, like at the enemy spawn. Place your dispenser somewhere near his setup and he can keep and eye on it while you do other things, just don't have it to close so if an uber comes in and busts his stuff, he can rebuild off your dispenser. If you are running minis, place them within the other sentries field of fire to create a 'layered' defence. Obviously don't be afraid to upgrade another engis stuff if it is well placed.

Carry combo

Often you will see a med/whatever combo on your team who are totally ripping the enemy apart. While they seldom give two ♥♥♥♥♥ about you, moving in very close behind them gives many opportunities for setting up stuff in very forward positions. Occasionally the med may even throw you some heals.

My mate the Medic.

Usually you have to be totally dominating a server before a med is willing to do fun things with an engi, so you want to get a friend in for this stuff. That said, if you ask nicely, people are often willing to have fun. Kritzkreiged engi can be great, nobody sees it coming, your tinny little pistol becomes a wrecking machine with a kritz, widowmaker is also great. If you do get kritzed randomly, don't be afraid to go balls out aggressive, you can often pick up a few kills.
Breaking through chokes to get behind the lines is hard, unless you are invincible. Being a ninja is one way to get through the lines, the other is to uber up and bulldoze past. Try and do as much damage as you can to keep people back/get some kills, remember the goal though. Once the uber runs out, generally you and the med want to separate to make it harder to track you down, he can attack the lines from behind to recharge fast with the ubersaw and you continue on to get a sneaky tele up.
This last one is just plain fun. On blue you build a lvl 3 sentry during setup time, then pick it up and the med latches onto you and follows you out the gate. Move forward as far as you can to either a perfect ultra aggressive spot or till the med has to uber, then put the sentry down and get it up as fast as you can. You and the med use your ubered bodies to protect the sentry as it comes up. Done right, you now have a lvl 3 sentry set up right in the middle of the enemy force about 15 seconds after the game starts, you sitting behind it with full metal. Results are generally hilarious.

Like most classes, if you get the chance and you aren't doing anything more important, nothing wrong with throwing some pistol spam at heavies if they are at long range. Your pistol is pretty much the equal of a minigun from far out and you don't have to wind up or spin down. Crouch down and move back and forth to make yourself a harder target and try and keep their focus, normally a sniper or spy will pick them off if they stay spun up somewheres that can be seen from range. Pistol spam is especially good for GRU heavies, its nice fat damage and it makes a great noise when you hit.
Up close from front on, you are 90% sure going to die, badly. You cant take a heavy front on without some B.S. luck, even if he is terrible. So be smart and don't get into that position. Flank or rear attacks only. Justice for preference, shotgun in a pinch, though not unsupported by other players if you can help it.
Heavies often do an interesting thing if they take a lot of damage while shooting, they spin down and try and run away. So if you do have to engage them with a shotgun, try and flank while they are spun up, you usually get 2 shots before they work out they are taking big damage, then they spin down and you can get more shots into them, trick here is not to let up the attack unless things are going very badly for you. If you empty your shotgun and he's still not dead, its much harder for him to hit you if you are running around his fat arse flailing with your wrench/gunslinger than if you were just running away.

Oh, and if you catch a heavy eating a sandvich, you pretty much have to taunt kill him, not only for the lols, but also because tauntkills are pretty much the only thing that will kill the fat buggers in time if you don't have a few revenge crits to spare.

Demos generally come in 3 flavours, sticky/nade demos, demoknights with sword and shield and stickyjumper/caber trolls.

Starting at the bottom you have caber trolls, you see them a fair bit in pub play and they can be surprisingly effective at times. The simple thing to do is just stay the hell away from them, watch where they are jumping to and try and keep players between you and them, they just want a kill and then to either die or go back to spawn. More fun is to try and skeet shoot them out of the air with justice crits or hammer them with pistol spam while backpedaling like a fiend. Sentries, the wrangler or to a lesser extent minisentries will also put a fair dint in anyone trying to do a lot of jumping.

Demoknights can be a bit more dangerous if they are a bit skilled, smart ones will be using nades against your sentries and trying to melee you. The demoknight is set up for fairly short range, shotguns are generally good against them, though all bullets really. Hammering a demoknight in the face with a shotgun when he is 2 steps while he charges at you is always a good laugh.

Most dangerous are generally the stock loadout demos, they are massively powerful in the right hands and are pretty much perfectly set up to combat sentries, do like ive mentioned earlier and take the fight right to them as soon as they start attacking the sentry, closer the better. Melee range is a great place to fight demos even if you are using a shottie, anything but their melee will usually kill them and only sometimes you at point blank if you have hit them first. Similar story with just flat ambushing them as the come round a corner. Get into point blank range as fast as possible and start swinging.

Snipers come in 2 basic flavours, huntsman snipers and rifle snipers.

Huntsman snipers are good against minis and the better ones can easily headshot at point blank. Rifle snipers have the huge disadvantage of tunnel vision when they are scoped in. A great sniper will often basically have see you = kill you.

Throwing pistol spam at them at range will often knock their aim off and running at a sniper dodging and jumping wildly while spamming the pistol can be a workable tactic against an average sniper, just don't run right at them and give them a chance to get an easy shot on you.
Normally though, the best way to deal with snipers is to flank hard and come up on them from a direction they cant see while scoped in. Scoped in snipers are my main source of taunt kills.

Make note also, of if a sniper has the razorback equipped, if he does that mean he has pretty much nothing that is good at medium/short range, great shotgun range. Again, trick is to get into that range without being seen. Avoid the obvious spots snipers are going to be watching and if you do have to cross, remember, the second mouse gets the cheese. If someone runs in front of you and the sniper kills him, you will have a window of a second or so before he will be able to get another shot off.

As you gaze across the battlefield you briefly lock eyes with your enemy, steely eyed and rock jawed he matches your gaze unflinchingly, two samurai titans of unending battle, both battered but unbroken. The wreckage of countless shattered warmachines strewn about yet constantly being gathered and hammered back into yet another device in the service of carnage to be thrown back into the neverending maelstrom of battle.
Sorry, I've been up all night ♥♥♥♥♥♥♥ with this guide, something like that had to pop out somewheres.

As most engis in pub like to turtle, you probably wont go up against many of them toe to toe. That said, your pistol is a great anti-building weapon. Be smart, first kill the dispenser, then the sentry. If the engi has his stuff spaced out, hit the sentry a few times so he goes to it, then kill the dispenser.

If you come up against an engi silly enough to block his sentries fire with a dispenser, take full advantage. Hide behind the dispenser, kill the engi, then the sentry, then the dispenser.
You can kill an unattended sentry with your wrench if you are smart and a bit lucky, you just have to keep moving around behind as it tracks you.
Using an enemy sentry to kill its engineer is a bit easier, its generally a suicide run, but damn funny. Just get the enemy engi between you and his sentry.

Any chance you get to take out teles, you should, but remember an engi really doesn't have the close in damage potential to camp a tele exit, that's something best left to other classes.

Dealing with minisentries
Deserves its own little heading, but its really very simple, they don't have much health, shoot them and they will die, fast. The worst thing you can do with a minisentry is ignore it.

One simple statement: The most powerful class in TF2 is the Medic. Hands down. Pretty much every game is won by medics in one way, shape or form. Don't care how pro you think you are at any class, a good medic is the greatest asset any team can have. If you ever play highlander or 6v6 you will know the best call you can ever make is 'medic down.' So you really, really, really want to show your respect for medics by targeting them above all others at every opportunity you get.
Medics also don't get many chances to kill things so they really, really want you to get into ubersaw range so they have an excuse to stick it in you. So try and stay the hell out of point blank range unless you are sure you can get that medic kill.

When all is said and done though, you shouldn't get many chances to kill a good medic. If you get the opportunity to ambush, in a team sense, its often worth suiciding into a pack of enemies just to kill a med so they cant use their uber/kritz on your team. One of the better times to go after medics, oddly enough, is just as an uber finishes. Again, justice crits are great, but never be afraid to throw the kitchen sink at an enemy med the second his uber runs out. Hopefully the rest of your team has the same idea.
Don't make the mistake of bothering to shoot at ubered people, all you do is attract their attention, ive killed more than a few meds by just standing directly behind them and waiting for an uber to finish so I could unload.

Shooting someone being healed by a med with a pistol is worse than pointless unless you know they have just taken huge damage, all you will do is charge the meds uber faster.

If you do manage to engage a med 1v1, you will know fast if he is good. The good ones will know the arc of the needlegun well, and in the right hands, its a decent weapon. In the wrong hands though, they will usually just drop needles at your feet. Never make the mistake of running directly at a med shooting, combat medic 101 is backpedal and shoot needles at whatever offends you. Dodge and circle strafe as much as possible. Stay out of melee range because again, every med is melee hungry. Medium range is great, needles get harder to use the longer the range, and the pistol is perfect for medium range.

Pyros. They used to be seen as a scrub class and still are by some people but its pretty hard to deny the flat out usefulness of a good pyro. Rockets, nades and arrows get thrown back with more power than they went out with, ubers get stalled, heavies get axtinguished and the flaregun can be srs bzns in the right hands.
That said, pyros are still mainly a close range beast so you best option is to hit them from medium/long ranges. The old 'backpedal madly while shooting' is a favourite against pyros and it works, against flaregunners not so well, but generally the pyro is going to try and get in close and do damage. Pistol at long/medium ranges, shottie when/if they are close. If you are ambushed by a pyro, shottie should be your goto gun, 2/3 good hits and they will die, so if you are using the justice, you really, really don't want to miss. If you do get attacked at close range by a pryo, get the hell out if you can though, its usually the best option if it is there.

Due to their short range, pyros are also nicely vulnerable to all sorts of sentries, fighting pyros around your sentries is generally the best way to go, you want to be in the sentries field of fire, but far enough away the pryo has to choose between you and the sentry. Same goes for minis, make them choose between the 2 targets that are both attacking them, usually they will go after a mini rather than and engi, if they take it out, just rebuild, move away and keep shooting them.

Again, a very powerful well rounded class, a good solli is usually what I view as my biggest threat in tf2. Perfect for taking out sentries at range, direct hit can 1 shot minis, don't be surprised if you see a lot of direct hits on the other team if you are really tearing it up with minis.

If a solli is hitting your sentry at range, make the choice to either try and save it (remember, repair only damage) or go after the solli, if you can keep the solli focused on your sentry long enough, someone will usually pick him off. As ive stated before, a solli with the normal rocket launcher cant actually kill a lvl 2 sentry by himself it the engi is behind the sentry and keeps his cool. Other option is to hammer at the solli, they only hold 4> shots, if you have just seen a solli fire 4 rockets, he is out, you can safely go at him front on for a little while if he has a backpack.
Again, flank, ambush, attack the rear, though due to their higher heath a close in fight with a solli is often a dodgy prospect.

You can usually tell a higher quality solli by the way they move, the less skilled ones walk, the better ones fly, bouncing from wall to wall. This can actually be good for a minisentry engi, they will often get themselves hammered hard flying over a minisentry they didn't know was there. With a bit of skill, justice crits are also great against any flying enemies, a solid 150 damage hit is usually enough for them to die from fall damage when they hit the ground.

Sollis are also great for just dumping minis anywhere when you try and run away, they only hold 4 in the rocket launcher, its going to take at least 2 to kill your mini, that's 2 they aren't shooting at you.

Spies are meant to be the hard counter to engi, though I seem to dom more spies than any other class. This may be because often in pub you will have 3 bad spies and 1 good one on the team, but for whatever reason, generally I find spies to be more annoying than problematic. TF2 101 kiddies: The team needs at most 2 spies on a 12 player team. If there are already 2 spies, any more will just make the other team more watchful and ergo, are more harm than good. Learn to play medic, its actually fun and you will be the guy who is responsible for actually winning the game, rather than the 4th spy on a losing team.

Picking the good spies from the bad:
Whatever the loadout, bad spies will pick crap disguises (always scout against a team with no scouts, disguise as medic and chase the single enemy med around calling medic) and run right at their intended targets, usually in the complete opposite direction to the rest of the team. They also like to try and hide in corners. Against a bad spy, shoot the corners first.

Good spies will be a lot more crafty, disguises that change often, moving with the enemy team, looking in the same direction, etc. Good spies also have an interesting way of moving. A good spy wants to move in places other players don't so they don't get bumped, so on rails, jumping on rocks, generally moving on top of objects it would be easier to run round and taking longer paths.
So if you see a pryo running along a rail, he is probably a spy.

First rule of killing spies is shoot/wrench everybody, spycheck every damn person you see, then do it again.

Second rule is: Don't stand near your sentry if you can help it. Spies wont stab you if you are standing 10m from your sentry but still in clear view of it, they will get shot by the sentry.

Third rule is: Backstabs are reeeeeeeealy dodgy. A backstab can be from just about any direction on your screen and still a backstab for them. More than a few times have I had a spy literally stab me in the forehead while standing in front of me and have it register as a backstab. So fighting spies in melee can be a real crapshoot at times. Close range shottie work is often better than wrench, though the wrench is still good, just don't be surprised if lady luck decides to screw you.

Fourth rule is: Hunt the filthy scum and give them no respite. No matter what sort of spy, unless they are close to help, keep on hammering at them if you know where they are. Even deadringers have limited health or have to uncloak, once a spy is invisible, they are hard to find, but cant attack for at least a second or two. So just keep hammering them.
Also, seeing a teammate hammering at a possible spy, will usually cause more teammates to do likewise. So the longer you shoot the spy, the more people will join in.

Generally I don't run the pomson unless im having real problems with DR spies, that said, if they are a real problem then just spycheck everything you see with the pomson.
Sentries are good for telling if there is a DR spy around (no kill/assist recorded on the sentry), though it is a mixed blessing, all you know is that there is a DR spy who was somewhere in the area of your sentry and that is dickall when all is said and done.
You have time to spin around during wrench swings if you are fast. Always keep at eye out.

Stairstabs, aka 'I saw dis reel smart spi thing on youtube and it is awesoom'
Worth mentioning because they can be a real pain, but are just laughable once you know how to counter them.
What happens is, the spy stands at the top of some stairs, waits for an enemy to run up at him, then jumps over his head and stabs while in the air. Due to the backstab mechanics, or lack thereof, this almost always counts as a backstab.
You will either chase a spy and he will run up a stair and then try it, or see a spy/one of your players (hint, its a spy) just standing at the top of a stair waiting for people to walk up.
Two counters here. 1: Just shoot the idiot, frontier justice especially will happily 1 shot most spies.
2: Start running up the stair like a good victim, then as he jumps, back out and start swinging/shooting. As long as you back out quick enough the spy will often be confused enough about why his unbeatable strat didn't work for you to just club him to death with your wrench. It really is just as simple as backing out at the right time. Then you have to taunt and possibly send him degrading messages through chat.

Scouts are one of the fastest, most agile and hardest hitting of all classes in TF2. A good scout is a really nasty thing to come up against. Luckily they are also very fragile, this means you usually wont see many scouts if you are playing 12v12 servers, there is just too much stuff for them to have to try and dodge, they are still about, but the smaller the server gets, the greater a threat a good scout is.

More than a few scouts hate playing against me, the main reason being: Minisentries. Scouts like to be able to move through a map at will, minisentries make large 'no go' sections all over the place, they can take them down, but it takes time/health and puts the scout in vulnerable positions. Scouts love nice open spaces to jump around and make ♥♥♥♥♥ out of themselves in, minis just ruin that for them.
So against scouts, spam minis, lots of minis, spam all the minis. You get the idea.

The other thing with scouts is if they take a decent amount of damage, they will just run off and get a health pack. Hammering them with pistol spam at range can be a good way to just get them to bugger off for a while, you will seldom kill them, but they will find something better to do.

You should pretty much never get the chance to ambush a scout from behind, they move too fast, you best ambush chance is to hide behind a corner when they are chasing you and hammer them in the face when they round the corner. Its dicey as the scout has such huge close range damage but scouts love to chase, if a scout goes after you, you either want to get to the protection of sentries or to other players, just running and hoping they go away just wont cut it.

So you have got to the point where you think you are ok at tf2, you can do well in quickplay servers, what are some simple steps to take to get better?
Note: This is going to be more general stuff than 100% engi related

Multiclassing.
Being decent with multiple classes will give you a lot better sense of how the game should be played. IMO every player should get to the point where they are at least a competent med so you can understand the basics of what a med can and cant do, med isn't that hard to do well with and it can be allot of fun. If you have having problems with spies, play a bit of spy and get decent at it, work out where spies are going to be going, what works, what doesn't, etc. Playing a bit of demo and solli will teach any engi what sentry spots are easy to take down and from where.
You get the idea, basically don't be a one trick pony.

Get off the valve servers
Valve servers and quickplay servers in general will have a lower class of players on than many of the other servers around. You want to find servers with lots of regulars, decent admins, higher quality players, etc. The quickest way to get better is to have your ♥♥♥♥ spanked hard, over and over every time you make a small mistake, this will teach you to stop making those small mistakes fast. Playing with crits turned off will also help your gameplay quite a bit, you realise what a crutch crits can be once you play without them.

Training maps
More for solli, demo, sniper and pyro reflect training than anything else. A bit of time on these maps will really polish your accuracy, there are some great ones out there, just poke around.

Youtube
There are some great vids out there for being a better anything. Great thing about this day and age is that anything you want to do, some yoyo has made a vid about it in great detail and put it up on youtube.

Comp play
Whether its pickup games or organised clan matches, comp play is another place where any small mistakes are going to be slapped down hard. I used to play a bit of 6v6, got sick of it because I find most people take it a bit too seriously, I now play regular highlander matches as engi and have heaps of fun. Team level tactics are huge in clan games, its a side you just don't see in pub play. Being involved in clan stuff, while some of it can be a headache, is generally heaps of fun and very rewarding.