Ok, let's break it down.
1. Play the tutorial. Then play Coop games against Easy AI. Then play Coop games against Intermediate AI. This should adequately teach you the basics of the game and how it proceeds. Intermediate bots are more cmpetent than quite a few human players I've seen, so there's that.
2. DO NOT DIE! This is your first priority. This is the basic lesson you should learn. Focus on it. Focus on not getting killed. Everything comes from that.
3. Not losing is more important than winning. Or in other words - avoid risks if you want to win. I can't stress this enough. Play safe, play carefully, avoid suicide runs, focus on not losing your lane instead of constantly trying for kills. Don't be totally passive, but don't go chasing people under their towers at level 2 because you just HAVE to get that kill. And if you're being pushed back don't try to kill soe minions while at 2 HP, losing those few minions will hurt you less than getting killed.
4. Win your lane (or at least don't lose it). That's your job early on. Park your arse in your lane and make sure you get more money than the other team. Try to kill the tower if you can, but don't get killed trying.
5. Learn to last hit. You may have noticed that only the last hit on a minion gives you money. This is called lasthitting and it's a crucial skill to acquire. Might seem small, but 20ish minions is worth one kill. That shit adds up. Also, constantly autoattacking your lane pushes it towards the enemy tower which in turn means it's easier for their teammates to come in from the river and kill you from behind. There is a time and place to push, but not all the time.
6. Don't worry about builds too much. Follow the reccomended builds at first until you get comfortable with the various items. The default builds for most champions are pretty solid. In time you'll see what you need (more damage? more health? etc.).
7. For advanced training, watch streams. Go to Own3d.tv or Twitch.tv and find a popular livestream. Just watch and you'll learn tons. Some streamers are better, some worse for this, but you can see a ton of advanced strategies and subtle things, like how to use wards, how to control the minion line, when to push, when to hug your tower, when to harass, when to be passive, etc.
Most important is experience, though. Pay attention to other players, especially the ones who are doing well. Don't get pissed when you lose, but try to see why you lost. What did they do that won them the game. If someone on your team is doing great, try to see what he is doing. It doesn't matter if he's using a champion you don't play, a lot of the general behaviour can be applied to any champion.
And finally, have fun, that's what really counts!
