[This tutorial is based on Linux Ubuntu Distro, but the tools used are widely available to be used for any other distro]

Lifehacker gave a nice tutorial on how to do DVD ripping under windows, with the help of a combination of shareware and free tools. It’s only fair to show that under Linux, this can done just as easily.

1) First we will copy & paste this commands in the terminal:
sudo apt-get install dvdrip subtitleripper ksubtitleripper gocr mplayer libdvdread3 debhelper fakeroot

2) After downloading and installing the necessary software and libraries are complete, we will need to issue this command: sudo /usr/share/doc/libdvdread3/install-css.sh which will download some more files and libraries.

3) Than go to Application –> Sound & Video –> dvd::rip for some dvd ripping goodness.

You can download dvd::rip from here: http://www.exit1.org/dvdrip/
For a more in depth guide on Dvd Ripping and transcoding under linux, Check out this document:
http://www.bunkus.org/dvdripping4linux/en/single/index.html