Because Windows 8 now ships on a vast variety of hardware that doesn't always have a disk drive (e.g. touch devices), Microsoft decided not to include DVD codec in their new operating system to make it cheaper. This leads to the problem that devices that actually do have a disk drive cannot play DVDs out of the box:
The easiest way to circumvent this problem is to install a third-party multimedia player that is able to play DVDs - for example the popular VideoLAN player (VLC Player) which is able to play nearly any multimedia format.
You can download it here.
After downloading the installer, double-click it and follow the instructions. Afterwards you can right-click the DVD again and open it with VLC:
A few days ago version 2.0 of the popular VLC media player was released, called Twoflower. Since it is not yet in the repositories, you have to add a repository if you want to update your present version.
Independent of your distribution, first log in as root:
On Linux Mint 12 and Ubuntu 11.10, add following repository:
Afterwards, update your sources list:
Finally, install VLC 2.0:
apt-get install vlc
On openSuSE 12.1, add following repository:
zypper ar http://download.videolan.org/pub/vlc/SuSE/12.1 VLC
Then refresh your sources:
And finally install VLC:
zypper in vlc
You can find the release notes for the new version on the VLC homepage: http://www.videolan.org/