*Go to the Contact view (View -> Contacts)
*Select the desired contact
*Make sure that you're either in the 'Business Card Mode' view,
  or the 'Linked Mode' view, so that you can see all the objects that's
  linked to the contact in the 'Linked To..' pane
 (To get more information on the views, please watch this training movie)
*Select the Organization that you want to un-link from the contact
*Hit the [delete] key on your keyboard
*You should now get the 'Unlink or Delete' dialogue window
*Click on the 'Unlink' button