Well, there's several ways to do it:
You could "capture" the video and the audio, but unless you already have the equipment to it, it can be an expensive endevour. But it would probably be the "cleanest" way to do it.
You could play the video, and mic the speakers.
You could buy the soundtrack and rip the song to MP3.
Which ever way you choose, be advised that that you are dealing with copyright material, and using it without permission is illegal!