I have just written this article. But there is also an easier solution.
This is the quick and dirty way for making Skype work on Ubuntu 13.04 running Nvidia drivers:
Just add this alias in your ~/.bashrc file:
alias skype='export LD_PRELOAD=/usr/lib/i386-linux-gnu/mesa/libGL.so.1 && /usr/bin/skype'
But, if you want to keep your terminal usable (demonize the process), add this alias to your ~/.bashrc:
alias skype='export LD_PRELOAD=/usr/lib/i386-linux-gnu/mesa/libGL.so.1 && nohup /usr/bin/skype &> /dev/null &'
Now, type skype in your terminal and it will launch the Skype Messenger.
It works with AMD drivers too.