ATI provides video drivers for both 32 and 64-bit Linux operating systems on their website amd.com. Once you download the installer, run it with administrative permissions and it will do the rest. Your video card should be automatically detected and the appropriate drivers installed.
Ubuntu is known for its compatibility and ease of use; installing most drivers doesn't even require any intervention on your part. Everything is mostly automatic. Ubuntu may not detect your ATI card automatically, however, in which case you'll need to manually acquire the drivers from ATI's website and install them.
Not all ATI cards are supported in all versions of Ubuntu. If you've tried installing ATI Linux drivers and you're still encountering problems, you may simply have to settle with using generic video drivers. While that's not ideal, it's because Linux doesn't have the widespread support enjoyed by other operating systems. You should check regularly for ATI driver updates and check the Ubuntu forums to see if others share your problem, a homebrew solution may be available.
ATI Card Not Installed
Check that your system actually has an ATI card installed. Because you have an AMD processor doesn't automatically mean you have an ATI card. The easiest way to check is by opening your computer case, or checking the documentation that came with your system. If you know you have an ATI card, reseat it in its slot -- a video card can pop out over time.
Sometimes video drivers can get corrupted with other Linux updates, such as those to the kernal. If you find Ubuntu stops booting properly, or your video settings are simply not working anymore, re-install the ATI drivers. Get the latest versions from ATI's website.