I like to use a waiter's corkscrew at home, but if you're not used to the way it operates or if you don't open lots of bottles of wine, you may find it difficult to use. Here's an excellent video equipment review from America's Test Kitchen, explaining and rating some of the many options available for getting those corks out.
(Some of the content on the ATK site is free and some requires a registration and/or subscription. This content is currently free, but that could change in the future.)
Click here for their video demo and review.
Update: You may also be interested in this review of an electric opener. I have a friend who owns this model, and it is super easy to use.