Most of the explanation is already at : http://www.wbitt.com/my-howtos/139-skype-on-fedora-11-64-bit-x8664.html

Download Skype for Linux. You will probably not find a 64 bit version. Download 32 bit version: skype-2.1.0.81-fc10.i586.rpm

Then install the following :

yum -y install pulseaudio-libs.i686 pulseaudio-libs-devel.i686 alsa-plugins-pulseaudio.i686 \
libv4l.i686   libXv.i686 libXv-devel.i686 libXScrnSaver.i686  libXScrnSaver-devel.i686    \
dbus-qt.i686 dbus-qt-devel.i686 qt.i686 qt-devel.i686

Now install skype:

yum -y localinstall skype-2.1.0.81-fc10.i586.rpm  --nogpgcheck

Then issue :

ldconfig

That’s all. Enjoy!