These are the current Federal Regulations. All states base their guidelines on federal regulations. Be familiar with these as they are applicable across the country and cover most of the basics.
Here is the AZGFD page with the current AZ regulations as well as an apprentice packet and other information. Arizona is pretty falconry friendly compared to most states but there are specific rules that you must know that apply only to Arizona falconry. The actual regulations themselves, R12-4-422 can be found here.
This is Commission Order 25 which specifies raptor take in AZ. CO25 lists which raptors are currently legal take for apprentices, general and master falconers and explains the non-resident take process which is different for each species.
Coming in to AZ from out of state? Here's some basics...
If you are coming for less than 30 days, you do not need a health certificate:
AZ Regs J(1)(c)
"Provide a health certificate for each raptor possessed under the out-of-state sport falconry license when the raptor is present in this state for more than 30 consecutive days. The health certificate may be issued after the date of the interstate importation, but shall have been issued no more than 30 consecutive days prior to the interstate importation."
Hunting licenses are required to practice falconry. AZ provides short-term ($20 per day) or annual ($160 from Jan 1 through Dec 31) non-resident hunting licenses. They are available online, at all Game and Fish offices, and at many sporting goods stores. This page provides the info on licensing details: