Get used to dying alot, the game at times is more like an RTS as you slam troops towards an objective and many die in the process.
Play a simple class that doesn't cause much stress, such as Medic. That way you're playing a vital role to the team, and you can see how other classes play and maneuver themselves around.
You don't throw grenades in TF2. The Demoman class has a grenade launcher + sticky bomb gun, but this isn't a game like Halo or Call of Duty where everyone has nades.
If you're unsure of yourself, play a local match against bots. That way you can practice aiming and how each weapon works. It's pretty much nothing like most shooters you're probably used to.
The community in the game is superb. The mic screamers and children are few and far between. Enjoy it because there aren't many games left like it.
Pick a map type (Control Point, Payload, etc) and stick with it. That way you're not confused as to what type of objectives you should be completing. Do this for awhile at least until you get more comfortable. I play on SourceOP 24/7 Goldrush. That's a Payload map where you push a cart over tracks on offense while Red defends. It's pretty fun.
Most of all have fun. It's one of the best shooters ever made (IMO).