Visit the U.S. Department of State's website at http://travel.state.gov/passport/forms/ds5504/ds5504_2663.html.
Fill out Form DS-5504 online and print it in black ink. You can alternatively print the form in black ink and then write on it in black pen.
Mail Form DS-5504 to the address given on the form, along with your passport, two recent color photographs and legal certification of your name change, such as a certified copy of your marriage certificate.