According to the United States Department of State, you can renew your passport by mail if the original is undamaged and can be submitted with your application, and was issued within the last 15 years when you were at least 16. You will need to follow the original passport regulations, such as getting a 2-by-2 photo.
Fill out form DS-82, which is available at the travel.state.gov website. Mail the form, and the other necessary information to the "Renew Passport" address on the form.
If you can't use DS-82, or you can't apply by mail, you must apply in person with the required identification, including the old passport, a birth certificate and valid government identification.
Pay the renewal fee. As of 2011, the renewal fee was $140 for adults and $120 for minors.