Since Skype (now Microsoft!) fails miserably to offer a 64bit package for Fedora, you’ll have to install i686 libs to accomodate for the crippled official package.
Here you go:
$ su -c 'yum install glibc.i686 alsa-lib.i686 \
libXv.i686 libXScrnSaver.i686 qt.i686 qt-x11.i686'
$ su -c 'rpm -Uvh skype*.rpm'
This will install a lot of 32bit stuff, but so it happens with closed software. It sucks.