Pretty straight forward really... 
Here's a quickly put together example. But it provides all the needed info.
Checkout the animation below i've made. Each step is shown on its own. Then a combined version, then with colour added.
Basically put, you're creating ovals, the selecting them and using the SELCTION/Transform Selection... function to reduce the size of the selection. When you've done this, and perhaps even moved the selection a little to create the porper crescent shape, you delete the selected area.
The same proceudre is done 2x. 1 for the main circle, and once for the thinner oval ring. The second oval ring is a duplicate of the first, that's been rotated 180 degrees. Then moved into position.
The only other specific thing you need to do is erase or select and delete the small area shown within the red circle in the animation.
After that, the separate parts are coloured. And if you wish, all layers Merged together -- except the BG layer. (not Flattened, Merged)
Any confusion on this, just ask. [honesty]
