Whats fastest way for me to earn IP?

buy an IP boost from the shop. otherwise grind out games until you have enough. remember that you get 1st win of the day IP boost everyday as well.

play games

I think Summoner's Rift games vs Players give the most IP but sometimes they take a long time. I play lots of bot games and ARAM. The IP is less but the time is usually consistent I suppose? I don't remember.

Buy X Day IP Boosts and grind bot games. You have an extremely slim chance of losing and games tend to end quickly, as long as the other players have any idea as to what they are doing.