Pros: You can use a multitude of different items -- almost anything hard, skinny, and long (hehe)
Cons: You need to be kind of strong, and maybe not mind a cork floating in your wine
This is simple enough -- it's what I tried to do with the breadstick. Just stick a very solid (again, more solid than a breadstick) item on top of the cork in question and just push, baby. Push like you're delivering triplets in a Hollywood rom-com!
A screwdriver, or a pen/pencil works very well. But the handle of a wooden spoon is ideal, as to not tear the cork up in the process. This torn-up cork will make drinking the wine… problematic.