Linux has many ways to make a personal DVD backup if you are comfortable using command line tools. If however you would rather use a graphical interface, there are three main contenders - K9Copy, AcidRip, and DVD::RIP.
In order to read commercial DVDs, you must have the libdvdcss2 file to read the encrypted files. This file is not in the default repositories, instead you will have to find the repositories that hold the media packages that cannot be included in the installation packages for legal reasons. For Ubuntu that is the Medibuntu repository. For Fedora, you can find the library in the DAG repository.
There are many different ways to backup DVDs in Linux via the command line. Many people would rather use the command line rather than a GUI because it gives the user more control over the encode. If however you are just looking for a quick backup, or you are not comfortable with the command line, there are three graphical programs that make the process easier.
K9Copy has the nicest GUI and is the easiest to use of all the DVD ripping software. It takes a full size DVD and either shrinks it down to a 4.7 GB ISO image or converts it to a smaller .avi file for portable devices.
K9Copy uses Mencoder and Mplayer as its backend. Other requirements are DVDauthor, libdvdread, growisofs, libhal, libdbus and libdbus-qt. If you are installing with apt, the dependencies will be installed automatically. If you use rpm packages, you may have to install the dependencies separately.
If you are just looking for a backup to burn to media, you open the DVD and choose to burn to .iso. You can then burn the .iso file with another application such as K3b. K9Copy has its own burning software, but it does not work as well as K3b or other burning software.
AcidRip is another wrapper for Mencoder and Mplayer, this one written in Perl. Although it has a GUI, it is not as sophisticated as K9Copy, but it does give you more control over your rip. You can change the codec and the bitrate, as well as other options.
If you are looking for a quick backup, AcidRip may not be right for you. It also has no documentation. Instead the author recommends that you use the mencoder and mplayer documentation. However, if you are familiar with basic video encoding, it should not be a problem. Direct copies are exact copies of the DVD. You have to change the encoding options to make the file small enough to fit on a 4.7 GB disk.
DVD::Rip does not use mencoder for it's backend. Instead it uses transcode for its encoding purposes. It does use mplayer for subtitle vobsub viewing but it is not required.
Like AcidRip, it is not meant for quick and easy encoding but there are many options that can be tweaked. DVD::Rip supports many different codecs such as divx4, divx5, xvid, xvidcvs, ffmpeg, fame, opendivx and mpeg2enc and it can also perform multi pass encoding, which allows for a better encode. Also, it does not automatically shrink the DVD to fit 4.7 GB media.
There are many different ways to make a personal DVD on Linux. AcidRip and DVD::Rip are designed for more intense video encoding. They are simply graphical wrappers for command line tools.
If you are looking for a simple, graphical DVD backup tool, I recommend K9Copy. The GUI is simple to understand and it automatically shrinks the output to fit a 4.7 GB disk.