You or the other driver are likely to call the police after the accident. When the officer arrives, he will likely ask for your vehicle registration, your license, and proof of insurance. Technically, Arizona is an at-fault state, so what happens depends on who actually caused the accident. If the other driver caused the accident, you're most likely fine.
That driver will notify your insurance company and take care of things from there. If you caused the accident and you don't have insurance, the best-case scenario is that the crash only damages you and your vehicle. That's the best-case scenario because you can pay your own bills as you see fit. However, if the other driver was injured, you can be sued for personal injury, and if the court finds you guilty, you will have to pay.
You will also need your insurance company to provide you with an SR22 certificate attesting that, in fact, you are insured and that you will continue to be insured. The first thing to understand is that it is illegal to operate a vehicle in the state of Arizona without a minimum amount of car insurance. It will take many years of driving history that is clean, without accidents and with a consistently insured vehicle before you can return to the lower insurance premiums you enjoyed before you got behind the wheel of that uninsured vehicle.