sudo yum install git

mkdir -p ~/git-repo
cd ~/git-repo
git clone https://github.com/martinrunge/muroa.git

Fedora Core does not include packages for ffmpeg and its libraries (libavcodec, libavformat and libavutil are needed by muroa) in its standard reporitories. They are available from the fusion repository, so make sure it is activated (see here how to do that: http://rpmfusion.org/Configuration):

sudo yum install cmake \
                 gcc-c++ \
                 gdb \
                 boost-devel \
                 sqlite-devel \
                 ffmpeg-devel \
                 alsa-lib-devel \
                 libao-devel \
                 log4cplus-devel \
                 avahi-devel \
                 avahi-qt4-devel \
                 qt-devel \
                 libsamplerate-devel \
                 zlib-devel \
                 taglib-devel

mkdir -p build-x86

cd build-x86
cmake ../muroa