Skype is only available as a 32 bit application on linux and in order to run skype on fedora 64 bit, you need to install the corresponding 32 bit packages. Prior to Fedora 13, installing the dependencies for Skype is quite easy, however in case of Fedora 13, there is a small hiccup.
Skype requires the installation of a package "nss-softokn-freebl". The native 64 bit version of this software in Fedora 13 is 3.12.4-19.fc13.x86_64 whereas the 32 bit version 3.12.4-17.fc13.i686 is older than the installed 64 bit native version. Consequently you cannot install an older 32 bit version of "nss-softokn-freebl" and yum terminates with an error. In order to avoid this issue, downgrade the 64 bit version of the corresponding software by issuing the following command in the terminal window:
sudo yum downgrade nss-softokn-freebl
The aforementioned command will downgrade nss-softokn-freebl to version 3.12.4-17.fc13.x86_64. After downgrading the above package, just issue the following commands in the terminal window to get Skype working under fedora 13.
sudo yum install alsa-lib.i686 libXv.i686 libXScrnSaver.i686 qt-x11.i686 qt.i686 --exclude nss-softokn-freebl.x86_64;sudo yum install skype-2.1.0.81-fc10.i586.rpm --nogpgcheck
Hopefully, this issue will be fixed in the subsequent releases of "nss-softokn-freebl" but for now, you can use the aforementioned technique to make Skype work normally. :)
Update:
The updated version 3.12.4-19.fc13.i686 of the package "nss-softokn-freebl" can be obtained from the following link:
With this, the aforementioned issue is obsolete.
