It never ceases to surprises me how many folks don't quite appreciate what a neat and clever tool this is. Maybe it's the simple design or how it looks against the veritable torture chamber of cork removal tools out there but I figured I'd take a shot at explaining how to go about using it for your standard issue cork removal needs.
Step 1: Remove Foil From Cork
Step 2: Insert Corkscrew
Step 3: The Really Cool Part.
Once you have the corkscrew setup like the first photo shows, all you do is pull up on the opposite end and the cork comes out fairly easily.