Unfortunately Handbrake is not in the (default) Fedora repositories, after much wasted time I have finally built it from source, here is what worked for me.
(warning) involves command line work
First install the dependencies needed for handbrake to compile (and build)
sudo yum groupinstall "Development Tools"
sudo yum install yasm zlib-devel bzip2-devel fribidi-devel dbus-glib-devel libgudev1-devel webkitgtk-devel libnotify-devel gstreamer-devel gstreamer-plugins-base-devel libsamplerate-devel libtheora-devel libass-devel libvorbis-devel libvorbis-devel libass-devel
Now check out the handbrake source code
svn checkout svn://svn.handbrake.fr/HandBrake/trunk handbrake
Now change into the directory that the source was downloaded to. From there we will configure build and install Handbrake
cd handbrake
./configure
cd build
gmake
sudo make install
Handbrake should now be within your menu, or you can run it from the command line
ghb
