You can visit the Clerk of Court's office and bring 2 passport photos, a birth certificate with a seal, and a picture id. It takes about six weeks to receive your passport.
Visit travel.state.gov for detailed information regarding applying for a passport and international travel. Where you apply for a passport depends on when you need your U.S. passport. Go to the Where to Apply page at travel.state.gov to determine where you apply based on when the passport is needed.