There are some decent videos on Youtube that give pointers for each class.
Personally, I found it helpful to stick to the Soldier and Scout while I was learning to play, and now I've started branching out to the other classes. (Haven't played in the last couple weeks due to it being crunch time at work combined with being sick.)
As a Scout, use your speed to your advantage. You'd be surprised how often you can take down a Heavy if you can flank him and attack from behind. A couple shotgun blasts or bats to the head and he's dead pretty quickly. Also, get used to double-jumping and use it to your advantage. You can end up in places where the other team isn't expecting to see you. Keep your distance from Pyros, as their flamethrower will do a number on you since your max health is low. Demomen can be a threat if you take a grenade to the face, but once you get used to moving and dodging it's not as bad. You're not well equipped to take down sentry guns, but you're fast enough that you might be able to shoot the Engineer before he builds it. If you're at close range and you empty your scattergun, don't be afraid to switch to the bat, especially against enemies like the Sniper and Medic who aren't expecting to be mixing it up.
Also, when you're a Scout don't waste the teleporters. Leave them for slower characters like Heavies.