With Fedora being on the bleeding-edge and not caring much about proprietary software support while the open-source graphics drivers continue to evolve, sometimes it can be a bit of a headache installing the AMD Catalyst/fglrx driver on the newest Fedora release, but generally it's possible.
For those that have upgraded to Fedora 21 since its release last month, you can get the latest Catalyst 14.12 binary blob working.
The open-source AMD Linux graphics driver advanced a lot in 2014 and is closer to performance parity, but if that doesn't cut it and you want to use the proprietary driver, there's a new guide courtesy of Red Hat intern Levente Kurusa.
Levente Kurusa has posted to his blog a guide for setting up the Catalyst driver on Fedora 21. You need to download the RHEL7 AMD driver package, enable DKMS support, use aticonfig to generate a config file, make some modifications to the fglrx_drv.so file, make some modifications to libglx.so, setting some environment variables so GNOME's Clutter will recognize the OpenGL driver, optionally switch over to lightdm instead of GDM, and then reboot. It's not trivial installing Catalyst on Fedora 21, but it's possible, at least for now until the xorg-server or Linux kernel is upgraded and the ABI breaks again (as it's still generally being a few month turnaround time for AMD to support new kernel and xorg-server interfaces).