You just need to find a recording software, download it, and record yourself drawing. That is, the screen of course. You may choose to just record your coloring, or maybe record your drawing from scratch.
Then when you're done, edit it by speeding it up and perhaps adding music.
It's simple, really. You just need to make sure you've got the time to finish it in one run, unless you want to edit out the pauses later.
The drawing program does not matter. As I said, you just need a recording software. Try Hypercam, maybe? Or any of those the others suggested.