Good advice ijack
If your distro has drivers for your card you'll want to try them first, ubuntu should volunteer to install the driver for you.
If you have a yum/rpm redhat based distro, like Fedora, use http://rpmfusion.org/
On ubuntu the proprietary driver thingy should pop up and offer to install the proprietary driver for ya if it's available or you can try it by hand with apt-get / dpkg.
I'm not sure about SuSE, I think they have something similar that provides proprietary stuff.
You'll want to backup your xorg.conf first and have your console and ssh ready to fix things if the ATI driver breaks your ubuntu GUI.
You should also be real careful about running .run files from the internet there's a lot of viruses and trojans out there, even for Linux, they're rare but they do exist. Always Virus scan with clamAV and avg or kasperky or whatever for linux and check the checksums and sigs first.