No matter where you apply for your passport, the procedure is the same. You will always need to present the same documentation and fill out the same forms. A list of the necessary documents can be found at the State Department's website.
U.S. passports are still issued by the U.S. Department of State in Washington, D.C., but Arizona residents can use their local services in connection with all of their passport needs. Scottsdale residents, for example, can go to the One Civic Center Building to handle passport requests.
Arizona residents can usually apply for passports from their home city. To apply for a passport in Arizona, take all of the necessary documents---such as passport forms, a birth certificate, proof of social security, photos and government-issued ID---to the local office that handles passport applications. In Phoenix, that office is the Superior Court of Maricopa County.