You can only use reasonable physical force needed at the time to protect yourself. If you hit back based on verbal threats or start the fight, then physical force is usually not justified. See A.R.S. § 13-404. Whether the force is reasonable depends on each case. For example, you can use deadly force to protect yourself against deadly force but that would not be justified if someone just punches you. This usually means you can use the same amount of force that the other person uses.
It is important to keep in mind that claiming self defense will not automatically let you off for fighting back. For example, if the other person starts the fight but in the middle wants to stop, you must also stop fighting. If you continue to hit him, you most likely will not be excused for self defense. You do not have a duty to run away after someone hits you. But if you do try to run away but can’t escape and your only option is to fight back, then self defense will most likely be justified.

You should think about the danger that the person is putting you in, and respond with an amount of force that would protect yourself from it. For example, if someone is hitting you, you can would expect to be possibly injured, but not killed by the attack. Your reasonable response would be to hit the person back or injure them, but killing them would go to far. If someone came at you with a gun, then there might be a real threat to your life, and you could use whatever force you need, potentially even killing the person, to protect yourself.

The bottom line is that if you respond with a reasonable amount of force in your situation, self-defense completely protects you from doing something illegal. This means that you can not get in trouble for it at all. If, on the other hand, you go too far (using too much force), only then do you become liable for your actions.