Let's say you're opening a bottle of wine with a corkscrew and the cork breaks before its out. Believe it or not, it is possible to get a broken cork out of a wine bottle, or even if you can't quite get the cork out, you can still get the wine out, which is the most important thing.
Step 1:
Unscrew the corkscrew from the cork.
Step 2:
Try screwing the corkscrew into the cork again. Screw it in about a half-dozen times until it feels like it has a good grip.
Step 3:
Pull the cork out gently. If you're lucky it should come out like a whole cork. If it doesn't work after a couple tries, or it breaks up, go on to the next step.
Step 4:
Push the broken cork into the bottle. Use the handle of a wood spoon or screwdriver or something like that. Do it gently so the wine doesn't splash.
Step 5:
Place a filter like a cheesecloth or a coffee filter over a decanter or pitcher or another container that can hold the wine.
Step 6:
Fasten the filter with string or a rubber band.
Step 7:
Pour the wine through the filter slowly. The filter will catch any pieces of cork that are floating in the wine.
Step 8:
Drink up. You'll want to finish the bottle because the cork is still stuck in the bottle, unless you have a bottle stopper handy.