Then I can't give you specific instructions, but I can tell you'll need to find a program that rips and converts. For OSX I use handbrake. It'll turn DVDs into .mpegs, .avi, .ogm...
From there you'll need something to isolate the clip and export it as a series of images (I use QTpro). Take that series and open it as a gif in your favorite gif editor (I use fireworks). Tweak and export.