No paper work required. Just be not otherwise excluded from owning a gun. Become familliar with the laws of Arizona. http://www.azdps.gov/Services/Concealed_Weapons/
On April 16, 2010, governor Jan Brewer signed into law a bill that legalizes the carrying of concealed firearms and other weapons in most places without a permit for adults over 21 years of age. Arizona will still issue concealed carry permits for purposes of reciprocity for carrying concealed weapons in other states and permits will still be required for carrying in certain sensitive areas within Arizona such as in bars or on school grounds. Open carry without a permit will still be legal in most places for 18-20 year-olds, and for emancipated juveniles. This law will take effect July 29, 2010. Arizona is only the third state in modern U.S. history (after Vermont and Alaska) to allow the carrying of concealed weapons without a permit, and it is the first state with a large urban population to do so.