Here's the process in AZ.
There is no tax on the private sale of vehicles.
For your own protection I strongly recommend the following:
1 - A bill of sale (even for $1.00), with the date and time of the sale, that says you are selling the car AZ IS with no warranties or guarantees of any kind. Signed by both parties, in duplicate, and you keep one.
2 - On the back of the title, you MUST (by law) enter the current odometer reading, check the odometer boxes, AND put in the name and address of the buyer, AND have your signature notarized. Photocopy both sides of the title. Do not let the title remain "open" (without the buyer information).
3 - When you hand over the title and the keys, you MUST (by law) remove your license plate(s) from the car BEFORE the new owner drives off with it. This should not be a problem for the new owner as a temporary sticker is available online or at any DMV office. She can get it with the VIN of the car. You do not want anybody driving around with a license plate that has your name on the record. Once she gets it home she'll have no choice but to go to the DMV and transfer the title and get new plates. DO NOT ACCEPT ANY SOB STORY THAT RESULTS IN HER DRIVING OFF WITH YOUR LICENSE PLATE.
4 - On the back of the registration form there is a notice to the DMV about the sale of the vehicle. You MUST (by law) fill it out and send it it. Make a photo copy of both sides before you mail it.
5 - Keep the documentation on file indefinitely. You never know when things can come back to haunt you.