Do people really use DVDs any more? Optical media such as CDs and DVDs have mostly proven themselves as being easily scratched and damaged, bothersome to store, and easy to misplace. Many music and movie lovers have moved to storing their collection on a harddrive, where the files can be played from any device and safely backed up.
Download the appropriate Linux installer, depending on your distribution and architecture (32 bit or 64 bit) and allow Software Installer to install the necessary files.
The easiest way to use HandBrake, unless you know a lot about video encoding, is to take advantage of its presets:
Re-encoding video is one of the more intensive processes for a computer, so this will take some time. But when it's finished, you'll have a movie file that you can play without the pesky DVD.