If you fly direct from the United States to Italy, then the border control officer will place a stamp inside your passport which indicates the moment you entered the country.
If for some reason you will not be traveling direct to Italy but rather first landing in another European Union country before entering Italy, then your passport will lack a necessary entry stamp called a “timbro”. In such cases, it is necessary for you to go to the Questura (Police Station) of your comune within eight days of entry into Italy to file a Declaration of Presence within the country, known as a “Dichiarazione di Presenza”.
As stated earlier, the timbro in your passport is your declaration of presence if you entered Italy directly from your home country and did not have a connecting flight through another EU country. The officer at the Questura will want to know why you are there and why you feel you need to make a Dichiarazione di Presenza, so you will need to bring all your paperwork with you to show him/her that you are in Italy to apply for Italian citizenship and will need the Dichiarazione di Presenza to obtain residency status at your selected comune.
You will also need to bring a 3×4 photo of yourself and proof that you are staying somewhere in Italy. This can be your lease agreement or a letter of hospitality issued by your host. Sometimes, they want to see a dichiarazione di presenza even if you have an entry stamp on your passport.
Further details: How to report entering Italy