Going to keep this one quick, here’s a quick guide for installing Skype on Debian Jessie. This is based on version 4.3.0.37, but should just need a URL switch for newer versions.
wget http://download.skype.com/linux/skype-4.3.0.37.tar.bz2 tar xvf skype-4.3.0.37.tar.bz2 cd skype-4.3.0.37 sudo aptitude install libxv1:i386 sudo aptitude install libxss1:i386 sudo aptitude install libqtdbus4:i386 sudo aptitude install libqtwebkit4:i386 ./skype
From there, you should be able to log in and chat away. Details on autostart (on login) to follow.