Illustrator - a VERY basic question

I'm admittedly a greenhorn when it comes to vector based programs and have a seemingly ridiculous problem: when creating two partially overlapping objects (let's say 2 circles), how do I manipulate (in this case fill with differents colors) the segments seperately? I've tried selecting the paths of one or both circles, then applying the "transform" - "divide" command, but cannot seem to apply seperate fills to the 3 segments. What am I missing here???

You have to ungroup them first. Object - Ungroup