Assuming that theyare an Arizona resident as well:
I, (name of purchaser), did on (date) receive one (make/model/serial number of gun) from (name of seller) for the purchase price of $xxx.
(purchaser signs this receipt) you keep this as a receipt for your gun.
I, (name of seller), did on (date) receive $xxx from (name of purchaser)for the purchase of one (make/model/serial number of gun).
(seller signs this receipt) purchaser keeps this as a receipt for their money.
If the transfer is a gift such as there is no transfer of money - just leave out the purchase price part and have them sign a receipt for receiving the gun.
The document is called a bill of sale and can be typed, handwritten, can be on parchment or toilet paper - so long as it is dated and signed.