how do my parents go about emancipating me?

The Arizona law that discusses emancipation says " a minor who wishes to be emancipated may file for an emancipation order with the clerk of the court in the county in which the minor resides if all of the following apply".  To look at the law, go to A.R.S. § 12-2451. The minor petitions the court for emancipation.

Also, you might want to look at the Emancipation Laws section on this website.