I am an American, but currently hold residency in Berlin, Germany with a work visa. My fiance is from Florence, Italy where we will be getting married this month, and where I will be moving to. How do I change my residency to Florence?
Basically, you just move there. Under directive 2004/38/EC, you have the legal right to accompany your spouse everywhere in the EU except for Italy (because you are the spouse of an Italian). Italy has extended this right to the family members of its citizens, however, so you are in luck: you do not have to meet any financial requirements, language requirements, or social integration requirements. Once you are married, you are almost completely protected against deportation; failure to comply with administrative requirements such as registration can only be punished with a fine, just as if you were an Italian citizen.
You can inform the German authorities that you are leaving. I don't know whether it's required to de-register from your municipality, but I suppose it's a good idea. If I were in your shoes I'd also approach the foreigners' office, but I wouldn't be surprised if they said there's no need for official notification.
When you get to Italy, you'll need to visit the immigration office there, to apply for your residence card. You may also be required to register with the municipality.