RPM packages are available from RPMFusion for all supported Fedora releases. The package works fine on both i686 and x86_64 systems and already contains support for the S3 Texture compression library for open source drivers (
radeon, intel and nouveau) along with all the required libraries to start playing with Steam games.
To install, after enabling the RPMFusion repositories, simply issue
sudo yum install steam
Note: There is also a staging repository where additional options are added to the package, like Valve's xpad driver and packages for running the SteamOS client in SteamOS mode. These features might not end up in RPMFusion. The repository is available at negativo17.org.
Source:
Valve