DVDs are encrypted, so you'd need to break the encryption first which (strictly speaking) is illegal. But yeah, it's possible. You'll need some sort of software though, i.e. it's not as simple as just dragging the audio files to your hard drive like you'd do with an audio CD. As for which software you'd need, I really don't know (I don't do this sort of thing very often).
An alternative method (which I've used before) is to get a double-male audio cord thing (sorry, no idea what it's called) and plug one end into your DVD player's headphone jack and the other into your computer's microphone jack. Then then hit play on the DVD player, and go into Audacity
on your computer and make sure the input settings are good, and then start the movie. Then when the movie is over you can hit stop in Audacity and crop out what you want, and export it as an mp3 or a wav or whatever. The downside to doing it this way is it must be done in real time, i.e. it takes 2 hours to record audio from a 2-hour movie, etc. And the resulting sound quality is not perfect (though it is pretty good).