You can install Skype on Fedora from its repository, which for me is the best way to do it, specially to stay with the latest stable versions.

All you need to do is to create a file named skype.repo and lacated in:

/etc/yum.repos.d/

And this file should have this content.

[skype] name=Skype Repository baseurl=http://download.skype.com/linux/repos/fedora/updates/i586/ gpgkey=http://www.skype.com/products/skype/linux/rpm-public-key.asc

once this file is saved all you need to do is run the next command

yum install skype

This worked for me in F7