Hm, if you're in the United States(mainly Virginia), you can go to your particular county's court website and search "name change". There, they should provide you with information regarding where your local courthouse is/what to bring/etc.
I had to type up an Order of Name Change, a Petition of Name Change(your court's website should have examples of these available for your use) and then get them notarized. That part is free if you go through your bank. If you are a customer at a particular bank, they often have a notary on staff who will work with you for no charge. Cool, huh?
Then I just brought my paperwork and payment to my local courthouse and had it filed. A few weeks later, the order was mailed to me, already signed by a judge. No court appearances or anything! It was pretty simple.
Some states require you to take out a few ads to show that you've had it changed to any potential debt collectors and whatnot, but it reall varies from place-to-place.