1. Install needed dependencies:
$ sudo yum install alsa-lib.i686 fontconfig.i686 freetype.i686 glib2.i686 libSM.i686 libXScrnSaver.i686 libXi.i686 libXrandr.i686 libXrender.i686 libXv.i686 libstdc++.i686 pulseaudio-libs.i686 qt.i686 qt-x11.i686 zlib.i686 qtwebkit.i686
2. Download the Skype rpm via command line as follows:
$ wget -c http://download.skype.com/linux/skype-4.3.0.37-fedora.i586.rpm
3. Install Skype via command line:
$ sudo yum localinstall skype-4.3.0.37-fedora.i586.rpm
4. Start using it! 🙂
