are you referring to DVD-A?
The music is usually stored as AC-3 audio.
I've never messed with a DVD-A yet. Not sure if it has the same encryptions as the DVD videos. If it does. the encryption needs to be broken before you can do anything. If it does not have encryption then things would be much simpler. You can use
BeSweet AC3-mp3 converter.
It is not as simple as converting a CDDA to mp3. You may need to remember to downsample the songs from 48khz to 44.1khz before encoding as well.
If you are referring to the songs on a DVD video. You will need to decode the whole movie (roughly 4 gigs of data), then demux the .VOB files to seperate Audio and Video files, then convert the ac3 to mp3.
a few related previous threads
Mp3 convertors
dvd decryption