You can rip the audio from a DVD, but it might not be perfect. The easiest way, in my opinion, is to use HandBrake to rip the DVD into a video file format, then load it into VLC Media Player to split the audio from the video (demux). Both HandBrake and VLC Media Player are free and both work on Mac and Windows. You might be disappointed with the quality of your audio though. I think you can use Audacity for this too, but I don't know that software well. It's also free if you want to try it. Have you tried checking YouTube for the soundtrack?
@Rusty, it depends on how obscure/popular the movie was and what year it was shot.
If the movie was popular, then the soundtracks may be sold individually as music records. I have an album of Hans Zimmer's famous soundtracks. His music is like a marriage of instrumental pop and classical music.
Hey there Reggie. I have a fantastic suggestion for you. I was listening to the Piano Guys, and their rendition of the Pirates of the Caribbean came up. It was better than the original, in my own opinion. The point is, you can find lots of covers of soundtracks on the internet.