EXTERMINATE.
Anyway, I think a tip for the the general game is to spy-check anybody you see running in the opposite direction (Towards your base) with either a flame thrower or a normal gun. No Team damage means no worrying about upsetting anybody. If anything they'd be glad you're doing it.
Engi's are mostly good for point-defense, though you can set up "Mobile defense" strategy by setting up wherever the heaviest fighting is. Also, anybody running towards your turret is probably a spy, dispensers are useful to teammates, so spy-check to be sure.
Heavies are heavies. Shoot stuff. A lot. Good for defense and pumping lots of bullets where needed.
Demomen are good at area denial and laying traps. They are also good at rooting out campers with the ability to bounce grenades around corners.
Soldiers can be good at area denial, but not as easily as the demoman. Best to shoot at people's feet, but then if they jump in time they can avoid a lot of the damage plus go flying.
Pyros are
really good at spy checking. One short blast is all that's needed. They can also be useful for sweet, sweet ironic deaths. Use your blastback on a crit rocket and watch the blood shower.
Medics are usually found with Heavies. A Heavy+Medic combo act as the game's tank, even more so then the normal heavy. Ubercharges are pretty much used to run into a heavily defended area and kill as much stuff as possible before your charge wears off.
Scouts are good for capturing stuff, as you may expect, scouting. They capture points at twice the rate and, if played correctly, can (literally) run circles around the enemy, shooting them many times before then can get a hit.
Spies are somewhat difficult to do well. Make sure never to run at someone like you're going to kill them, because they will probably notice. Use the cloak to get into the enemy base, then set up a disguise and wreak havoc. They are good at sabotage and killing campers, causing confusion and panic in the enemy lines, destroying Engineer buildings and killing anybody giving your team problems.
Snipers are good for giving the other team problems. Sit back (Preferably against a wall) and shoot anything of the other color that moves. Hopefully in the head.