There are 9 classes with unique attributes such as health, run speed, weapons, and other special abilities. Each class has 3 weapons, a Primary, a Secondary, and a Meele weapon (spy and engineer also have a fourth equip-able for a special ability).
General info: Switch weapons with scroll wheel or numbers 1-3. 'q' quickswitches between last weapon. You can walk through your friendly team members. There is no friendly fire, you cannot hurt team members with your weapons. Explosive weapons like rockets and the demoman's weapons can damage only the player shooting them if they explode too close. Explosive projectiles cannot shoot through a friendly sentry gun/buildings, though they will not damage the building.
This is a team based shooter, and as such game modes have varying objectives, killing enemies is good, but the objective is your main goal, you just might have to kill enemies on the way, why is this relevant? When attacking don't just go running off around the map killing whoever you find, instead go with a group of your team members towards the objective. If your whole team happends to die, it will be more effective to wait, and go in as a group to a dangerous zone otherwise you'll be outmatched many to one and die with the numbers against you, then the next team member will be outmatched many to one again and so on. When defending, almost always go straight to the objective to help your team defend it there.
Note also: damage to enemies is not dependent on where you hit them, so no need to aim for the head (unless using a sniper rifle), a bullet to the head is as good as a bullet to the foot in all other cases, so aim right at your enemies. Note: if using the soldier, aim rockets at your enemies feet though, foot is a direct hit, and if you miss (people can dodge!), the explosion against the ground will still damage them.