The Skype is not available for Fedora 64 bits. If you try to install .rpm package available from Skype in your 64 bit machine the installation will fail. So, in order to install Skype in 64 bit machine you need to add some libraries from x86. After installing this library, you can download the Skype .rpm package from the Skype official website and install in your x86 system. Go to terminal and paste the following command to add the library.
su -c 'yum install libXScrnSaver.i?86 libX11.i?86 libv4l.i?86 alsa-plugins-pulseaudio.i?86 qt-x11.i?86 libXv.i?86'
Download Skype and Enjoy!!