As has been said, the best way to get into LoL is to try it with friends or play the game with a mentor friend. Krypt0nian recently just started playing i think. (where did he go? maybe league killed him)
you can also watch some esport VODs. a recent fun one was NALCS - CLG v TSM w3:
http://www.youtube.com/watch?v=tqpFjeFHiE0. See if you feel anything.
To get into the game without friends:
1. do the tutorials
2. play a beginner vs ai game or two
3. read a beginners guide e.g. something like this:
http://www.solomid.net/guides.php?g=25755. many beginner videos kinda suck and i should go make one myself.
4. play some more beginner vs ai games with that new knowledge until you are level 4-5 (should take maybe 10 games
5. enter the scary world of PvP
- there will be a lot of information and a lot of different champions - to avoid info-overload and fear, just focus on your own play and your own champion. Focus on improving mechanical things like, last hitting, aiming skills, positioning, kiting etc. Take time to think about the items and what they do.
6. keep playing, read guides on specific champions you play or ones that give you trouble (a good website could be lolpro.com, solomid.net or lolking.net) and think about the items and what they are useful for.
good luck!
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something important that many guides seem to miss
Minion aggro mechanics:
They follow a priority list of targets:
1. Cries for help from a friendly champion
2. Closest enemy target
If you make an "auto attack" (which is the action performed when you right click on an enemy) on a champion - the champion will issue a cry for help. Every minion has an "aggro radius", which is the area in which it can hear cries for help from enemy champions. If a minion can hear a cry for help, itll start attacking you until a few seconds after you stop auto attacking the champion.
Tower Aggro Mechanics:
Priority list:
1. Cries for help from friendly champion
2. cannon minion
3. melee minion
4. caster minion
unlike minions, if you deal ANY damage to an enemy champion within the aggro radius of their tower, there will be a cry for help and the tower will attack you