The first part is the installation.
Fire up your preferred program to do installation of packages on Ubuntu. I use Synaptic, there are a couple of other options.
You need to install this list of packages, and all of their dependencies. I found the list by searching for "chess" in Synaptic, and ticking the boxes next to each of the programs (right click and select "Mark for Installation"):
Let the programs install. I found that I had to reboot after installing everything -- you actually just need to restart the X server and font server, but rebooting is probably simpler and almost as fast.