You will need to supply proof that you are a United States citizen. This requires one of the following documents: an expired passport, a certified copy of your birth certificate (please note a simple copy is not enough, it must be certified), a certification of birth if you were born abroad to parents that were US citizens, a copy of your naturalization certificate or an actual certificate of citizenship. As of April 2011, the new rules state that your birth certificate must have the full names of both parents included on the document.
You will also need to verify your identity. The following documents are allowed as proof of your identity: a former United States passport, your driver's license, a government ID (this can be state or federal), a naturalization certificate, or a military ID. Dependents of military personnel can also use their military ID's for this purpose. If you are using a driver's license, note that it must be current and it must also show you current physical address.
Several forms of secondary identification documents can be used if you do not have the necessary documents. These secondary identity verification documents include: your Social Security card, a library card, a credit card or an employee ID. Note that these can also be used if accompanied by another form of ID, such as your driver's license or birth certificate. You can also bring a witness to stand for you. They must fill out Form DS-71 in the presence of a passport agent and verify your identity.
You will also need to submit a current photo of yourself with your passport application and verifying documents. This photo needs to be a headshot and you must face the camera. Some passport agencies have a camera on-site to take your picture while you are applying, but just in case, you should have a current, printed photograph of yourself that can be used for your passport. The photo must be 2 inches-by-2 inches, taken in front of a plain white background and it must have been taken within the last six months.