Forward; As I've become more experienced and skilled playing this game I've begun to notice more and more the lack of experience and skill in my fellow GG2 players when it comes to playing the engineer. I think this has to do with the fact that hardly any long time players use the engy as their "main" character (makes sense seeing as how back in the old days the engy was useless), meaning most of today's engineers are noobs that don't know their wrench from their hard hat. As such, I've decided to create a comprehensive guide to the playing of the engineer, for both veteran and noob alike. I'm not saying I'm the ultimate master of playing the engy, but I think I know enough to potentially improve some peoples game. So, if you're interested in learning how to kick ass with one of the most unkillable and versatile classes in the game please read on.
Overview of the EngineerThe Engineer is a powerful character because of one feature he has that no other class does; that is, of course, the sentry gun. It is not JUST a gun, however. It is also a shield, a holder of the front line, a trap, a stalling tool, and even a demoralizer. There's very little a sentry can't do if you're creative. And, best of all, it pretty much has infinite health because you can just remake it every time it blows up. Beyond that, the engineer also has average HP and running speed, both useful for placing turrets in combat zones. The shotgun is also devastating when combined with the firepower of the sentry gun, and an invaluable tool for stopping the engineers natural enemy, the Spy. For all his natural talents, however, what makes or breaks an engineer ultimately comes down to how he uses the sentry gun.
Turret-fu OR how I learned to stop worrying and love the right clickThere are two distinct styles of playing an engineer. Both are amazing in a given situation. The two kinds are defensive and offensive. A good engineer should understand both, and, just as importantly, know when to play which. The first thing you should understand is that even if you play offensively the engy is not a scorer. If you can make it into the enemies base your time would be better spent distracting the enemy or spawn camping long enough for a faster character to get the intel. If you can get yourself into a good position behind enemy lines you can easily earn your team SEVERAL points just though distraction and blocking valuable paths. On the other hand, a good defensive engineer can easily prevent just as many scores by the opponent single-handedly. Knowing what is needed at any given time is mostly a matter of experience, and is hard to put into words. If you see a lot of scouts and spies, or the intel is not defended at all defense is needed. If it looks defended you may want to attack. If you aren't sure what to do just play it safe and defend. For now, though, lets move on to something that IS based on facts and easy to explain. Lets go over proper sentry placement and combat strategy for both kinds of engy, starting with the most common variety.
Playing a defensive engy First thing you do when you spawn as a defensive engineer is immediately run to the intel and immediately plop a sentry in the location that most efficiently blocks every path to and from the intel. Almost every map (EVERY map in 2.0, I think) has at least two entries/exits to the intel room. A gun that only covers one or two but not all is useless; any spy or scout well just run down the undefended path the second they get the intel. Even for weak classes it takes a few seconds of constant sentry fire to kill them. A quick burst as they run by wont do anything. Here's some examples of good and bad placement

Numbered here are some sentry placements I often see in 2Dfort. This is purely for example and my comments here are applicable to any map.
#1 - terrible Sentry placement #1 is a perfect example of terrible sentry placement. The only character it could ever kill is a scout, and it only blocks the hardly-used upper path. Not only that, but any class can just run past it and easily survive. A scout could even go in AND out that way and live if he's fast enough.
#2 - bad Not as bad as #1, this still isn't very smart placement. It defends the bottom paths but leaves the intel wide open to spies and scouts. Only use this spot of your intel has another defender that you really trust.
#3 - What the hell are you thinking? I have no idea why people put sentries here. It's the worst single spot on the whole map to put it. There's no chance it well ever hit anybody for more than half a second.
#4 - bad same as #2
#5 - goodThis is a pretty good placement; not only does is have several seconds to shoot anybody coming up the lower path, but it also defends the upper path a little bit. It doesn't protect the top very well though.
#6 - just right! This is the best possible placement; it has several seconds of fire time on both the top AND bottom path. Assuming you're constantly shooting your shotgun down the stairs to spycheck no single character can survive long enough to get the intel. Scouts coming up the top well get shot the second they jump up and classes coming up are often so afraid of the sentry that they stand around until a pyro spawns and kills them from behind.
Now that you have a bit of an example, here are some
general rules of defensive sentry placement:
•ALWAYS place them so they defend every path to and from the intel. If you can't do that place them so they defend either every path to it or every path from it, whichever you can get the most seconds of sustained fire.
•Place them so that anybody has to go through at least 2 seconds of constant fire to get in and out with the intel, no matter how they move.
•ALWAYS SPY CHECK. NEVER STOP SHOOTING.
ALTERNATE BETWEEN EVERY PATH THEY COULD COME AT YOU FROM. DO NOT STAND STILL. see Taimat's post
If somebody somehow DOES get the intel and escape follow them and keep shooting your shotgun! If they die put a sentry directly under the dropped intel and shoot anybody who gets close to it. If the person who stole the intel is too far ahead to shoot turn around and set up new defenses. You don't want the intel undefended after they score.
Playing an offensive engy The first thing you do when you spawn as an offensive engy is make sure the intel is defended. If it isn't, immediately change to a defensive engy. If it IS defended, go to the front line of the battle and place your sentry as forward as you can get it without dying. (As you run to the front line be sure to leave a trail of sentries behind you. You'll be glad to have someplace to fall back to if you're surprised by a pyro.) More importantly than the mere firepower it well add to the fight your sentry well act like a shield for your allies and help direct fire away from your team-mates. Also, if all your team-mates die a lone sentry can often hold the front lines long enough for reinforcements to show up. When placing a sentry don't worry about it dying. In fact you WANT it to take damage so that your teammates don't have to take it. Remember, your sentry doesn't have to run all the way back from the spawn point if it dies.
Use choke points to your advantage. A sentry on the front line is useless if the enemy can just jump over it for very little damage. Sentries are devastating when put at the end of long straight hallways.
If you can somehow get all the way into the enemy base don't go for the intel right away. Leave it to the scouts to score. They can score twice in the time it takes you to run it back once. Instead place your sentry in such a way that nobody can leave the enemy spawn (or at least one of the enemy spawns) without taking a large amount of damage. This can be done on any map and is useful mostly as a distraction and delay tactic. The easy kills you get are just icing on the cake. If the enemy starts spawning as soldiers and snipers and doing "shoot, heal, shoot, heal" cycles give yourself a pat on the back, you just took several enemies off the front line! The more people you can sucker into trying to kill you the better. And don't forget to spycheck! A lucky backstab could ruin all your fun.
That's all for now. This is already a wall of text, much longer than I thought it would be.
Hopefully somebody well learn something from this. If anybody else has some tips or questions feel free to post them. If you want my opinion on good sentry placement on a given map post a picture of it and I'll gladly comply.
Good luck, my friends, and godspeed.