I recently switched from using OpenSuse 12, to using Ubuntu 13.04 on my desktop machine at work. In order to get everything working correctly I had to use the latest ATI beta drivers (13.3 Beta).
After you unzip the downloaded file, simply run:
Initially the install script errored out, after it failed to locate ‘version.h’, so before I could successfully complete the driver install, I had to run:
Since these are beta drivers, they have a watermark in the lower right hand corner of each monitor. Â The solution to removing that watermark can be found here.
If you have dual monitors as I do, once you boot into ubuntu you will want to configure them with the ATI Control Center:
In order to get the latest version of Gnome you can add the Gnome3 team ppa’s:
# sudo apt-get update
# sudo apt-get upgrade
If  you want access to the latest bleeding edge applications and utilities , you can add the Ricotz testing ppa’s as well:
# sudo apt-get update
# sudo apt-get upgrade
The Ricotz staging ppa’s can be used however, there is a chance that if you upgrade with these, you system may end up becoming unstable:
# sudo apt-get update
# sudo apt-get upgrade
Finally, I ran into a bug in Gnome where my entire desktop background was gray/white, in inorder to get that issue fixed I followed the advice given in the comments section of this Youtube video.