Because of the extremely helpful instructions on the leap motion site, I have been able to make good progress. I have gotten the leap motion SDK hooked up to my project and have begun experimenting with the hand tracking. While eventually I would like to include a proper hand model, for now I have just been drawing out the joint positions. Below is a photo of my current representation of a hand. The blue spheres represent the joints in the hand, while the green sphere is the center of the palm.
I also have a short video of what happens when I wiggle my palm over the controller.
Since things have been going pretty well I am going to now move onto using this data in an actual virtual setting.