The QGIS instructions for building from source are targeted at Ubuntu, but they translate fairly well to Fedora. Here’s a quick guide:

Instead of preparing apt as they say, use yum or Package Manager to install these packages:

• cmake
• bison
• flex
• grass-devel
• geos-devel
• PyQt4-devel
• gsl-devel
• qwt-devel
• gdal-devel

There may be few that I already had installed on my system and missed; if you run configure below and find missing dependencies, run yum search <whatever> in a terminal to look for it. Make sure you install any relevant -devel packages as well.