Comment 15 for bug 1262238

I've just checked AMD's website, and it seems that they support your card only in their legacy driver which, however, doesn't support new xservers.

http://support.amd.com/en-us/download/desktop/legacy?product=Legacy2&os=Linux%20x86_64

That driver should work well with the kernel (Linux 3.2) and xserver (1.11) that come by default in Ubuntu 12.04 (not in the point releases though).

If you download the installer from that page, you can then follow these steps:
1) extract the zip archive
2) Open a terminal and get to the directory where the extracted installer is, then type
sudo sh name_of_the_installer --buildpkg Ubuntu/precise
3) This will build deb packages for you, which you will be able to install (only the fglrx package and the fglrx-amdcccle packages are useful to you)

I hope it helps.