There are a lot of ways to play Engi, offensive, defensive, support.
Offense, you can build up stuff (lvl 3 sentry , lvl 3 Tele Entrance) and try to penetrate the enemy base to drop a tele exit. Once you do, you can build a dispenser and upgrade it asap. Now if the area is clear, just go get yourself killed, or if you feel like you have enough ammo laying around, go ahead and destroy and rebuild your sentry. Another way to play on the offense is by using angles and corners. Build up a lvl 3 Dispenser and lvl 3 Sentry, then place the sentry in a spot where you can be sure to fire away at enemies, but where they cannot hit your engi if you stand to the side or behind the sentry. Place your dispenser near enough to recover your ammo without having to move, allowing you to just smack away for repairs due to the sentry damage taken.
Or just go suicidal with a mini sentry and just toss it in the middle of firefights and kill as many people as possible. hahah
Defense, protecting critical locations and choke points is key. Build up lvl 3 dispenser asap, and then your lvl 3 sentry. Using corners and angles for protection can help, and since it is a choke point, your team mates will love the dispenser. If you have a wrangler and have a large enough distance away from possible enemy intrusions, you can perform spy checks by firing a few rounds and a rocket at possible spies.
Support, well thats mainly using your teleports and dispenser in a smart way, build your teles in a place that you know it wont normally get destroyed, and build the exit in a good spot, not too deep, not too far back, and drop the dispenser near it too so your team knows to recover with it. You can also build a sentry there for safe keeping, or place your sentry on the offense.
Code
Sentry //(wall)
.......<Player Dispenser Repair from an off angel, use the wall as cover
Sentry
^Player^
Dispenser
Use the sentry as cover, a height advantage is usually better for this set up.