Taken from http://linuxinternetworks.com/applications/how-to-install-skype-on-centos6-rhel6/

Run update and install wget

yum update
yum install wget

Install the dependencies and download the skype for enterprise linux

yum install libXi.so.6 libXss.so.1 libasound.so.2 libXv.so.1 libSM.so.6 libXrender.so.
wget http://download.skype.com/linux/skype-2.2.0.35-fedora.i586.rpm
yum localinstall --nogpgcheck ./skype-*.rpm

Sometimes skype will not start, the only solution to start the skype is replacing the /usr/bin/skype with the download static skype:

wget http://download.skype.com/linux/skype_static-2.2.0.35.tar.bz2
tar xvf skype_static-x.x.x.x.tar.bz2
cp skype_static-2.2.0.35/skype /usr/bin/skype
cp: overwrite '/usr/bin/skype' ? Y

Now its clear. You can access the skype from Applicaions -> Internet -> Skype or type skype in your terminal.