From Quirkbooks:
The holidays are over, New Year's Eve is in the past, but all that leftover wine... it sits their in your fridge (or not, depending on the kind of wine), waiting to be finished. And perhaps, just perhaps in the midst of your revelry, you broke a cork or two. It happens....MORE
Never fear! The Worst-Case Scenario Survival Handbook: Holidays has you covered.
Examine the cork.
If the cork has broken due to improper corkscrew use, treat the broken cork as if it were whole. If the cork is pushed too far into the bottle, push it all the way in using any long, thin implement and proceed to "Make a filter," blow.
Reinsert the corkscrew.
Six half turns of the corkscrew will usually be enough to allow you to remove a full cork, but you may need fewer for a partial cork. Turn the corkscrew slowly to prevent further breakage.
Pull the cork out.
Pull up steadily on the corkscrew, being careul not to jerk the cork out of the bottol. If the cork remains in the bottle, bore a hole through the center of the cork, using the corkscrew as a drill.
If you've had to push the cork into the bottle:
Make a filter....
Going down market into the barley based tastes?
Here's "Worst-Case Wednesday: How To Keep Beverages Cool In The Desert"