Determine the copying restrictions in your region. U.S. residents have the right to copy media from a DVD they own as long as the copies are for private, non-commercial use -- in other words, as long as they are not distributed or sold.
Load the DVD into the computer's CD/DVD drive.
Adjust your audio settings to record from the audio output. For most computers running Windows, go to the "Control Panel," then the "Sound" window, which can be accessed through the "Hardware and Sound" heading. Select the "Sound" or "Properties" tab, find the "Sound Recording" box, and select your sound card's setting for direct recording from the drop down menu. The option may read "Wave Out," "Realtek HD Audio Input" or "Stereo Mix."
For Windows Vista, once you're in the Sound window, select the "Recording" tab. Right click on the list that pops up, and check the menu option, "Show Disabled Devices." Then find the setting option for your sound card as above.
For a computer with Mac OSX, install Audio Hijack and skip Step 4.
For all other computers, plug the input end of an audio connection cable into your headphone jack, then the output end into the microphone jack.
Open the recording program.
Open the DVD playing program. Fast forward to the part with the music you want to capture. Select "Play."
Press the "Record" button in your recording program.