Builds and strategy guides for champions
One for all: Leaguecraft. I practically learned play League of Legends keeping that site on my browser and playing LoL in window mode.
There tons of good guides, divided by champion. Each guide is voted by community so you can immediately distinguish between useful and garbage. And in addition every guide is linked to a patch version, so you know if they are outdated.
In addition you can check builds for League Of Legends at Moba Fire and another useful source of tips on specific champion styles and builds is of course the official forum NA or EU.