At the moment Skype.com does not provide and installation package for CentOS Linux. The closest package we can use to install Skype communicator on CentOS is is based on Fedora Linux. Navigate to http://www.skype.com/en/download-skype/skype-for-linux/ and download a Fedora i386 skype package. At the time of writing the package version is skype-126.96.36.199-fedora.i586.rpm. Once downloaded run the below yum command as a privileged user to install Skype on your CentOS linux system:
# yum localinstall skype-188.8.131.52-fedora.i586.rpm
The above command will install Skype along with any required prerequisites. After the installation you can start skype either from command line using the skype command:
or by clicking on Skype icon in the navigation menu.