Um...
Map types:
cp - Control Point
pl - Payload: Attack / Defense. Blu pushes cart and Red tries to stop them
koth - King of the Hill
ctf - Capture the Flag
dbs - Dodgeball
ph - Prophunt: One team gets disguised as random items and hides while the other team of pyros tries to find them. Using ammo damages yourself.
arena - Don't die
Scout:
Shoot things and stay moving generally. Not very fun to play when on a 32 person server in my opinions, but I stick to payload maps so scoots are almost never played.
Soldier:
ROCKET MAN and I think it's going to be a long long time. Pyros can reflect your rockets with airblast so if they are good watch out. Use your shotgun otherwise. Easy spam class.
Pyro:
If you don't have the Degreaser + Axetinguisher I seriously wouldn't even bother. Airblast is right click and you can extinguish friendlies (please do) and push sticky bombs and players back and reflect Rockets, Pipebombs, and Arrows.
Demoman:
Another generally easy spam class. Pipebombs and Sticky Bombs you can attach to anything just about. Right click to detonate. Watch for Pyros again although it is harder to reflect a pipebomb directly into someone.
Heavy:
Slow moving, highest HP class with a minigun. If you find a Sandvich you can eat it for full health or right click to make a medium medkit that will heal half of yours or someone elses HP. Rightclick spins your gun up. Jump rightclick can keep your movement up a bit.
Engineer:
Support / Defense. Build teleporters to move your team quickly, dispensers for health, ammo, and metal, and sentries. My most played by far only because I have terrible aim.
Medic:
Medic!
Medic!
Medic!
Meeeeeediiiiiiiiiiiiiiiiiiiiiic
Meeeeeeeeeeediiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiic
Rightclick at 100% turns you + someone invincible for 8(?) seconds but you can still be knocked and pushed around.
Sniper:
Obvious
Spy:
Sneak around, disguise as the other team, backstab someone or sap buildings and hope you don't get gibbed in the process.
In options somewhere I suggest you turn on auto reload and the medic auto-call function. Set it wherever.
My server list if you want

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Speaking of gibbing RANDOM CRITS ALL MY HATE. And whatever you do avoid Saigns.de and Nighteam servers.