In a nutshell, you want to take the rotations of the bones in the Leap Motion tracking data and apply them to the corresponding joints/bones in your character.
If your rig has a mechanim-compatible rig, you can use the LeapHandsAutoRig script. Just drop the script on your character and click AutoRig. If everything goes according to plan, this will hook up your character's hands to the Leap Motion controller in the scene in one click. But, and its a big but, you still have a lot of work to do to make things work well with a character rig. At first, your character's hands will just move to whatever random position relative the Leap Motion controller -- rubber banding the arms on the way. Really what you need is an IK solution to combine the animation derived from the Leap Motion data with character animation. We are experimenting with this, but don't have a finished solution to offer.