Primarily by selling RP (Riot Points). They do have some sponsors such as Coca-Cola (Source), but they thrive on something similar to a 'freemium' product. read more
Also noteworthy is just how badly League of Legends is trouncing the other big free-to-play games in North American, Dota 2 and Hearthstone. Both made the list, but way, way back in the pack: Dota 2 is at number nine with $136 million in revenues, while Hearthstone brought up the rear with $114 million. read more