Fedora comes with a built in video driver for most ATI graphic cards, but not all.
What you need to do is to install the proprietary ATI driver for your card.
For that you will need to get to a command prompt.
Holding down your ALT and CTRL keys and tapping the backspace should do that. ALT - CTRL - backspace is a command for killing the X server. If it should restart then try Alt - Ctrl - F1 which should give you one of the six available text logins. Log in as root.
What you need to do now is to activate one of the Fedora third party repositories that keep things not supplied with Fedora, usually for licence reasons.
Issue the command:
rpm -i http://rpm.livna.org/livna-release-8.rpm
and agree to whatever it suggests about authentication keys either now or later.
With that done, issue the command:
yum install kmod-fglrx xorg-x11-drv-fglrx-libs-32bit
That should install the ATI driver.
Restart your machine and you should be good to go.
If you haven't come across the command to reboot from the command prompt, it is: