Contact the Concealed Carry Unit at (800) 256-6280 and ask for an application packet. They mail it out to you.
N. An applicant shall demonstrate competence with a firearm through any of the following:
1. Completion of any firearms training program that is approved by the department of public safety and that is conducted by instructors who are authorized by the department of public safety or who possess current national rifle association instructor certifications in pistol and personal protection and who submit to a background investigation, including a check for warrants and a criminal history records check.
2. Completion of any firearms safety or training course or class that is available to the general public, that is offered by a law enforcement agency, a junior college, a college or a private or public institution, academy, organization or firearms training school and that is approved by the department of public safety.
3. Completion of any hunter education or hunter safety course approved by the Arizona game and fish department or a similar agency of another state.
4. Completion of any national rifle association firearms safety or training course.
5. Completion of any law enforcement firearms safety or training course or class that is offered for security guards, investigators, special deputies or other divisions or subdivisions of law enforcement or security enforcement and that is approved by the department of public safety.
6. Evidence of current military service or proof of honorable discharge or general discharge under honorable conditions from the United States armed forces.
7. A valid current or expired concealed weapon, firearm or handgun permit or license that is issued by another state or a political subdivision of another state and that has a training or testing requirement for initial issuance.
8. Completion of any governmental police agency firearms training course and qualification to carry a firearm in the course of normal police duties.
9. Completion of any other firearms training that the department of public safety deems acceptable.
If you don't already have something to satisfy the training requirements (DD-214, permit from your state, etc.) then take any NRA course. Easiest is FIRST Steps pistol (3 hours).
Have somebody local roll your prints and send the app packet back into them (they even supply the envelope).