First it depends on what card you have. You should have a look at this page:
As you can see, if you have anything less than ATI 8500 then you can use the DRI drivers. Check out their site and seach on google for how to use that driver.
However, if you have Radeon 8500 or newer, then you need to use the driver from ATI.com. Now Fedora Core 3 uses the Xorg 6.8, which is a version of the X window system. The latest ATI driver supports only upto Xorg 6.7. Which means that either you wait (like myself) for ATI to release a newer driver (hopefully this month) or you downgrade to Xorg 6.7 (highly INadvisable, will cause great trouble esp. since you're new).
So if you have a new card then keep checking the ati site for the release of a newer driver, when its released search on google, people would've written how to install it.