Watch the Champion Spotlight video on the Champion you wish to use
[Although some information is outdated, it will help you get a basic idea on how to play the champion]
Search youtube for "[Insert Champion Name Here] Guide", there should definitely be something for you to watch and learn. Try to make sure it's "S3" aka "Season 3" version. It's not the end of the world if it's not.
Mobafire and Solomid for rune and mastery guides. The author gives you a general description of why she or he chose those runes/masteries specifically.
Practice, Practice, Practice.