In order to playback a DVD you need to make use of commercial encryptions (also called codecs.) Actually Ubuntu calls them "non-free". The reality is these are patented and protected so people cannot just ripoff a DVD. Which is not true at all since pretty much any computer can play DVDs and thus can copy all the data. Anyway, because Ubuntu is by default for free software, it doesn't include all the necessary DVD stuff. This being said, they provide 100% of all the necessary code, pre-compiled and all you have to do is install it all with apt-get as follow.

(You must be root to run all those commands: sudo su - and enter your password in a console)

apt-get install ubuntu-restricted-extras
wget --output-document=/etc/apt/sources.list.d/medibuntu.list http://www.medibuntu.org/sources.list.d/$(lsb_release -cs).list
apt-get update
apt-get --yes --allow-unauthenticated install medibuntu-keyring
apt-get update
apt-get --yes install app-install-data-medibuntu apport-hooks-medibuntu
apt-get install libdvdcss2
apt-get install w64codecs

As I was at it (before I got to libdvdcss2) I also installed a few other things such as:

sudo apt-get install frei0r-plugins libfftw3-bin libfftw3-dev libroar-compat2 slv2-jack