When I tried to install the Debian Skype package from their website I received an error message “Wrong architecture ‘i386′”. It is way easier to install Skype directly from the command line, just enter these commands on a 64-bit system:

dpkg --add-architecture i386 apt-get update wget -O skype-install.deb http://www.skype.com/go/getskype-linux-deb dpkg -i skype-install.deb apt-get -f install

This will install Skype and all needed 32-bit libraries on a Debian 64-bit installation. Great also for automated installs of Skype. See https://wiki.debian.org/skype for more information.