User blog comment:Sam 3010/Ability Detail Project 1A/@comment-134746-20110304231613/@comment-569195-20110305000554

Doesn't LoL have a built in screen capture button? I found a post by Phreak:

F12 does take a screenshot. You have to rename the files after the game, or they will get overwritten in the next game you play. They are stored here (Riot Games\League of Legends\game). People seem to say it's in an annoying file format but GIMP works to open it.

I think FRAPS is free too and you can make videos with it.