Step 1:
Before leaving the US you will have to go to or contact your nearest Italian Consulate to get an Atto Notorio this is an oath which is sworn in front of two witnesses and notarized by the Italian Consular stating that there are no legal impediments to the marriage according to the laws to which the person concerned is subject to in the United States.
You may have to have your documents translated but the Italian Consulate will give you a list of translators who are qualified to do this.

The Atto Notorio also states that there are no impediments for the person requesting to marry in Italy according to Article 116 comma 2 (art. 85, 86, 87 number 1, 2 & 4) of the Italian Civil Code. Basically these refer to you not being mentally insane, not related in any way and my personal favourite that you haven’t tried or been convicted for killing a partner or another person.

You will need to get your documents Birth Certificates, previous Marriage Certificates and Decree Absolute, Death Certificates of a previous spouse translated and authenticated, the Italian Consular will give you the name of a registered translator for this service.

If you are living in the UK, the above Atto Notorio must be underwritten in the UK before an UK Notary.
You can contact De Pinna Notaries studio in London; they will provide also the translation into Italian.
I do not know what the fee for the Atto Notorio will be.

Step 2:
About a month before coming to Italy you should also book an appointment at the American Embassy in Rome.
You should also download the Nulla Osta Form, fill it in but don’t sign it.
The fee for the Nulla Osta can be paid in US$ in cash or by credit card.

Step 3:
Once you have your prized Nulla Osta they should be legalized by the Ufficio Legalizzazioni of the Prefettura in Rome: Via Ostiense, 131L, 2nd floor, Scala B, Rome - open Monday, Wednesday and Friday, 9:00am-12:00pm.
(you will need to get two Marca da Bollo (administration stamp) to the value of €14.62 at a tobacconist (tabaccaio).

Once all of these documents have been prepared, you will have to send us a copy via email, so we can check if everything is in order, and then bring the original documents with you when you will be travelling over here to get married.