How is Ifluence Points awarded in league of legends. I understand when one wins he gets more IP and if the stats are better during the game they get more. But how does one become able to "farm" or get the most IP possible and why?
There is a first win of the day Bonus every 22 hours which you should get as fast as possible (so you can reset the timer sooner). You can play a coop vs AI match to ensure you will get it as fast as possible. This bonus gives you an additional 150ip.
This is the first and most important thing you need to consider.
You can see every IP reward here: http://leagueoflegends.wikia.com/wiki/Influence_Points
If you are interested in farming IP then play dominion a lot! The games are shorter and you get bonus IP for finishing the fast. (You have to try and win a lot though). If you win in under 20 minutes you actually get more IP (unlike any other mode in League of Legends). Also as you can see dominion has the highest base ip reward in the game. Summoner's Rift is only better as the game lasts longer..
Note: Something that COULD possibly work for Ip farming if you don't care about defeats in dominion would be to have 4 friends with you and lose dominion on purpose. After 5 minutes the game would end and you would get the minimum amount of IP. But I suspect if you can lose 4 times in 20 minutes you would get more IP than winning 1 time in the same time.
But please note that you should never do this when you use matchmaking as you are ruining your teammates game. It's bad enough that you ruin your opponents game (although I think everyone can appreciate a 5 minute free win in dominion.)