From Skype 'File' menu >>> 'Sign Out' item does not work for you ?
On ne regarde pas l'avenir dans un rétroviseur !
IMac Intel Core i3 3.2 GHz - RAM 12 GB - OS 10.7.5
Skype 22.214.171.1246 + 126.96.36.1990
Logitech usb headset or Jabra 250 bt
this does not **bleep**ing work I'm really pissed .
What doesn't work?
If you're in the Skype programme and not the web page you have to go to the menu (at the top of the screen, not the top of the Skype window), as Foyan suggested in the post above yours. Select "File" (second on the left next to Skype) and then select the last item "Sign out". Don't select "Skype" and then Quit Skype, that just closes the programme.
It should work.