I got a webcam to play with at work and found that installing Skype on 64-bit Fedora wasn’t as easy as it should be. I did the usual yum install, and oddly it installed the package without a single dependency complaint… which was wrong. Run the below command as root to install all the dependencies you need to install the latest Skype beta.
yum -y install glibc.i686 alsa-lib.i686 libXv.i686 libXScrnSaver.i686 qt.i686 qt-x11.i686
Then, as root, do the following in the directory where you saved skype to:
yum -y install skype*
After that, you should be able to find skype by searching for it in Gnome and run it.