It's actually quite easy, if you have the right software and hardware.
First, you will need to rip the full video file off of the DVD. Use HandBreak and libdvdcss.dll for this. Oh, and hopefully you have access to a quad-core computer because otherwise, this step would take over an hour. This is because it takes a lot of computing power to break the copy protection of a DVD.
After you have the video file, use Freemake Video Convertor to convert the MP4 to a MP3. This step might also take some time, depending on how powerful your computer is. Once Freemake is finished converting the file, you'll have an MP3 containing the audio track of the DVD.