For this, the pen tool is definitely going to be your best friend. I’m afraid I’m not at my work computer at the moment, so I might give some of the wrong shortcuts, but I’ll double check either Saturday night or Sunday. The first thing you’re going to want to learn is how to use the pen tool, especially how to curve the line using points. You’ll probably use this for both the lines and the colors underneath. The next thing will be arranging. If you think of Illustrator like cutting out pieces of colored paper and arranging them how you like, you won’t be far off. Arranging basically decides which cut out is on top of the other cut outs. Another thing you might want to look into, depending on the version of Illustrator you’re using, is Livetrace. I usually hate using livetrace because you have very little control over what your doing, but a clean design can be converted with a little tweaking instead of having to trace it by hand.