Appeal
Ariz.R.Crim.P., Rule 30 & 31: A Defendant has 10 days from the date of their sentencing to file a "Notice of Appeal," and to prepare necessary documents for the appeal. The higher court then issues a "Briefing Schedule" which gives time limits for the parties for pleadings. The Court can either rule on the pleadings or can set the Appeal for "Oral Argument," where the parties show up to argue the case.

Post Conviction Relief Petition (PCR)
Ariz.R.Crim.P., Rule 32: If you feel that there were constitutional violations or newly discovered evidence has been found which supports your innocence, you then can file a "Post Conviction Relief Petition." Generally, the Defendant has 90 days from the date of "Sentencing" or the date of the last (final) appeal, to file a Post Conviction Relief Petition.