Basically a strategic game, control your "champion" around a map, taking turrets, pushing minion waves back etc etc (there's 80+ champs... so take your pick lol) get to level 30 on your summoner by winning games (this is you, basically)
and build your champions how you like with runes/masteries, create a good item build (as you kill minions/champs in game, you gain gold to buy items from the shop, use these to buff your champ up further and kick some ass) Either tank like a mofo or rape with damage, or somewhere in between, everyones playstyle is different.
You join up with a group of ur mates n go for it. 3v3 or 5v5, I'd deffo recommend it and I'd be happy to get you into it if need be jamie.
Sounds more confusing than it actually is, one game vs a bunch of bots and you'll get the hang of it.