To paraphrase Archimedes, give me a place to stand and a lever long enough, and I will open this %$#(&!!! bottle of wine.
Step 1: Materials
a bottle of wine
Ideally, you want a corkscrew like the one below. The flappy bit is the important thing.
Step 2: Remove the Foil
Step 3: Screw in the Corkscrew
If you watch the video at the end, you'll notice that I managed to screw in the corkscrew fairly badly off-center. Normally this makes it quit e a bit harder to get the cork out, but with this method, it doesn't make much difference.
Step 4: Remove the Cork
I've also included a video of the whole process so you can see how simple this really is.