Some information courtesy of MCC Voter Guide.
To register to vote you must meet the following simple requirements:
A Guide to Voter Rights in Arizona-
If you are having trouble logging in to the Service Arizona website, you can print off a Voter Registration Form (PDF) and fill it out with your new information. After you finish, mail the completed form to your County Recorder’s office and your information will be processed.
After you have successfully registered to vote you will receive a voter registration card in the mail within 4-6 weeks.
From Arizona Secretary of State
Arizona Voter Information Portal
https://my.arizona.vote/PortalList.aspx
Created by the Secretary of State's Office, here you can confirm your registration is ACTIVE, check your address and party affiliation, request a Ballot-by-Mail, and check the status of your Ballot-by-Mail.
All guides are available under the CC-BY-NC-SA license.