League of Legends (LoL) Question: Team Compostions/Tactics

This is a fantastic video on the subject by Valkrin, a challenger player in NA: https://www.youtube.com/watch?v=oNeH3bwCQKM

I'll summarize some of his key points in case you don't have time for the whole video.

The five basic types of team comps are:
1) Poke comp
2) Team Fight
3) Late Game
4) Early Game
5) Split push

Usually a team is a mix of these though. The things you should be looking to have when building a comp are:
1) Mix of magic and physical damage
2) Ranged poke and ranged attacks (to siege towers)
3) Some sort of engage / initiation (gap closers, ranged CC)
4) AoE waveclear for defending towers
5) Some late game scaling champions
6) Utility (speed boosts, shields, heals)
7) Frontline (tanky champions that can soak up damage)

Picking characters for things your team lacks is a good way to learn comps. If your team lacks CC pick a heavy CCer like Leona or if your team has a high early game presence like Renekton, Leblanc, and Caitlyn then go with a late game champ. Pick champs that check your teammates counters like picking Warwick to counter Shen. Team Comps are a lot easier to do when you play with people you know and/or a team that knows what kind of team they want like a heavy CC team or a team great at teamfights or split pushing.