You can obtain form DS-11 online or from a passport agency/acceptance facility. Fill it out and bring it with you, but do not sign it until you are directed to do so by the agent. You will need to provide both proof of U.S. citizenship and proof of identity.
According to the State Department, accepted proofs of U.S. citizenship include a certified birth certificate, a Consular Report of Birth Abroad, a certificate of citizenship or a naturalization certificate.
Acceptable identification proofs are a current government ID, valid drivers license, current military ID, undamaged U.S. passport or a naturalization certificate.
If you don't have any primary forms of government-issued identification (state or federal), you should bring as many forms of secondary identification as you can come up with. Acceptable secondary proofs of identification include a Social Security card, library card, credit card, employee ID or school ID.
The U.S. State Department allows you to have a witness with proper identification who can testify as to your identity.
Bring a photocopy of each piece of identification, whether it is primary or secondary. You will also need two passport photos. The photos must be in color, 2-inches-by-2-inches, recently taken and in everyday street clothes.