If you're running Mac OS X 10.7 "Lion," then Apple has taken measures to prevent doing this with screen-capture utilities.
You may be able to do it with iMovie (which should be included with your Mac, depending on when you bought it) and the free program Handbrake (available with a super-simple Google search).
Use Handbrake to convert the DVD to a format that iMovie understands (MP4, probably), then use iMovie to trim the video to just the specific section of video that you want, and export.