Installation is simple. First, add a rpmfusion. As it is described here you can just put this one line in the terminal:
su -c 'yum localinstall --nogpgcheck http://download1.rpmfusion.org/free/fedora/rpmfusion-free-release-$(rpm -E %fedora).noarch.rpm http://download1.rpmfusion.org/nonfree/fedora/rpmfusion-nonfree-release-$(rpm -E %fedora).noarch.rpm'
Next, install lpf-skype package.
su -c 'yum install lpf-skype'
Build and install Skype - just run lpf-skype (it can be run from gui or terminal) and follow the instructions. That’s all.
After installation i had a problem with no sound. In Skype sound options i saw only Virtual device. Here is my solution, install pulseaudio.
su -c 'yum install libv4l.i686 pulseaudio-libs.i686 alsa-plugins-pulseaudio.i686'
If Virtual device still will be seen in sound options then install pavucontrol.
su -c 'yum install pavucontrol'
It should help and sound options should have set PulseAdio server (local). You can also run pavucontrol to adjust the volume.