How to make a moon shape in Adobe Illustrator (for beginners)

Using the pathfinder tool, we can make the perfect moon shape in a few easy steps.

First, locate the Pathfinder tool. [Window > Pathfinder]

it should look like this:

I'm going to take two circles, one slightly larger than the other and place one on to of the other until it resembles a moon shape from the overlap:

(I drag the green over the pink)

Then click the second button on the pathfinder toolbox:

Resulting in this: 

Enjoy! You can play around with the circle shape, placement and size to get different desired moons. Gradients also look nice with this shape when executed properly.