The most popular map is a square. One base is bottom left, other is top right. There's 3 "lanes", top mid and bottom, which are paths to the other base. Along those paths are several turrets, which you pretty much have to destroy on the way to their base. Each lane has minions spawned, which are weak enemies that walk a straight path to the enemy base. Since they come in large numbers, once you've led them to a tower(turret), you're safe to attack it while it targets the minions. The goal is to get past all the turrets and destroy their "Nexus", the power source at their base.
You get 5 players per team, usually consisting of at least one of each playstyle. Carry, AP(mage-esque), support, jungle, whatever else. Tank maybe. Junglers generally play in the jungle, the area between lanes, which have some boss monsters that grant buffs when killed.
There's a few other maps(/game modes) but that's the main one.
But feel free to look it up yourself, I'm a complete noob to LoL.