Hello, this is my first post, as well as some of my first steps in the Creation Kit. I am trying to figure out how to create new killmoves for Skyrim. I have no idea how to do it, and was hoping someone could help start me off. Do I need an animation program, or does the Creation Kit have a built-in one?

Yep.

You could either go with Blender, or 3DS Max(up to 2012).