So you've broken the wine cork, nice one. Still, first things first, don't panic - the situation can be salvaged.
Gently work the corkscrew's spiral thread into what's left of the cork. Make sure it worms its way all the way through. Tug it out.
If the cork crumbles, decant the wine through muslin, or a tea strainer, into a decanter so as not to alert your guests to the accident.