In order to get married in Maricopa County, Arizona, you will need to apply for a marriage license before having your ceremony. I have posted a link below which will explain what is required.
As far as what will be required for immigration purposes, your husband would need to file an I-130 on your behalf and then you would have to go through consular processing (which requires you return to Mexico for an immigrant visa interview). This is assuming that you are not grandfathered under a provision of immigration law called 245(i). Additionally, because you have been in the U.S. for more than one year without permission you will need a waiver which requires you establish your husband would suffer extreme hardship if you are not able to return to the U.S. You will be able to apply for this waiver while in the United States beginning on March 4, 2013.
This is a very detailed process and the waiver requires meticulous documentation. I would highly recommend consulting with an immigration attorney who can discuss this process with you in more detail and outline the risks involved. An attorney can also help you determine whether you might be grandfathered under 245(i) which would mean you would not have to go to Mexico and could complete the green card process in the U.S.
Are you concerned about the marriage our you being able to stay in the country after you are married. I think you should talk with a lawyer to get answers to both of these questions and the questions and comments brought up by the other answers