First install the massive list of dependencies
yum install cmake bzip2-devel.i686 glew-devel.i686 mesa-libGL.i686 mesa-libGL-devel.i686 mesa-libGLU.i686 mesa-libGLU-devel.i686 mesa-libGLw.i686 mesa-libGLw-devel.i686 mesa-libOSMesa.i686 mesa-libOSMesa-devel.i686 alsa-lib.i686 alsa-lib-devel.i686 Cg libXxf86vm.i686 libXxf86vm-devel.i686 xorg-x11-proto-devel libX11.i686 libX11-devel.i686 xorg-x11-xtrans-devel libCg.i686 SDL.i686 SDL-devel.i686 sparsehash-devel freetype.i686 freetype-devel.i686 gtk2.i686 gtk2-devel.i686 zlib.i686 zlib-devel.i686 libjpeg-devel libjpeg wxGTK-devel.i686 portaudio.i686 portaudio-devel.i686 glib2-devel.i686 gdk-pixbuf2-devel.i686 atk-devel.i686 pango-devel.i686 cairo-devel.i686 libjpeg-turbo.i686 libjpeg-turbo-devel.i686 glibc-devel glibc-devel.i686 svn gcc-c++ libaio-devel libaio-devel.i686 mesa-libEGL-devel mesa-libEGL-devel.i686 mesa-libGLES-devel.i686 mesa-libGLES-devel glibc-devel.i686 glibc-devel
Next download the source from github
git clone https://github.com/PCSX2/pcsx2.git
Now its time to issue a few commands to set up our build directory
cd pcsx2-read-only && mkdir build && cd build
Time for cmake to get the ball rolling
cmake ../CMakeLists.txt -DCMAKE_BUILD_TYPE=Release && cd ..
Compile and install time, go get some coffee
make && make install
After PCSX2 finishes compiling and installing you can find it in the bin directory in the source directory. You can move the bin directory where ever you want for it's final resting place. Once you have it where you want it double click on the pcsx2 binary to start it up. This is what it should look like.
Or if you prefer there is a precompiled RPM for Fedora 19 on the official PCSX2 forums for download. The RPM and install directions can be found here. It's the latest release (1.1.0 as of this writing) where as compiling it from source will give you the latest and greatest bleeding edge features (or errors).