A new airplane can't fly until the weight of the paperwork generated by its development equals the weight of the plane itself. - Donald Douglas

From the Italian Consulate:

Documents required for application:

* Your Birth Certificate, with apostille attached and translated into Italian
* Your Parents Marriage Certificate with apostille attached and translated into Italian. Note: If your parents were not married at the time of your birth you do not qualify.
* Your Parents Birth Certificates with apostille attached and translated into Italian (if not from Italy)
* If you are claiming through a grandparent you will need your grandparent's marriage certificates with apostille attached and translated into Italian (if not from Italy) Note: If your grandparents were not married at the time of the birth of your parent you do not qualify.
* Your Grandparents Birth Certificates with apostille attached and translated into Italian (if not from Italy)
* Continue this process back to the ancestor who immigrated from Italy.
* For an Ancestor who immigrated to the US, you will need his/her naturalization records from the USCIS that shows that s/he did not become a US Citizen before their child was born.
* If USCIS responds with "No Records Found" you will have to contact NARA for the information.
* If NARA responds with "No Records Found" you will have to contact United States Census Department and ask for the census that took place before and after your Italian ancestor's child was born with the field report from the street they lived on.
* If the United States Census responds with "No Records Found" it will be assumed your Ancestor never became and US Citizen and retained his/her Italian citizenship and passed it on to their child.
* If there were any divorces in the line between you and your Italian ancestor, you will have to obtain all divorce records with apostille attached and translated into Italian. You will also need a "Certificate of Clerk - No Appeal"
* If any of the people mentioned above are deceased you will need their Death Certificates with apostille attached and translated into Italian (if not from Italy)
* All documents with errors must be corrected before being submitted. For example, if your Italian ancestor immigrated to the US and took on an "Americanized" name (Italian name: Giulia / American Name: Julia) and the Americanized name was used on any previously mentioned certificates the name will have to be corrected to match the name on their Italian Birth Certificate.
* A Photocopy of your current passport and ID
* Your application with sworn affidavit you never renounced your Italian Citizenship.

What have I gotten myself into? What is an apostille? A breath mint?

Wikipedia knows all

From the Wikipedia page Italian Nationality Law:

Special acquisition of citizenship through jus sanguinis

U.S. citizens, Canadians, Australians, New Zealanders, or others who are descended from an ancestor (parent, grandparent, great-grandparent, etc.) born in Italy may have a claim to Italian citizenship by descent. [1]

One must apply through the Italian consulate that has jurisdiction over their place of residence. Each consulate has slightly different procedures, requirements and wait time. Most importantly the criteria for iure sanguinis citizenship is the same.

* If you were born in the United States or Canada or any other Country where citizenship is acquired by birth (jus soli) and any one of the situations listed below pertain to you, you may be considered an Italian citizen. (For each category all conditions must be met).

* 1) Your father was officially recognized as an Italian citizen at the time of your birth and you never renounced your right to the Italian citizenship.
* 2) Your mother was officially recognized as an Italian citizen at the time of your birth, you were born after January 1st, 1948 and you never renounced your right to the Italian citizenship.
* 3) Your father was born in the United States or a Country other than Italy, your paternal grandfather was officially recognized as an Italian citizen at the time of his birth, neither you nor your father ever renounced your right to the Italian citizenship.
* 4) Your mother was born in the United States or a Country other than Italy, your maternal grandfather was officially recognized as an Italian citizen at the time of her birth, you were born after January 1, 1948 and neither you nor your mother ever renounced your right to the Italian citizenship.
* 5) Your paternal or maternal grandfather was born in the United States, your paternal great grandfather was officially recognized as an Italian citizen at the time of his birth, neither you nor your father nor your grandfather ever renounced your right to Italian citizenship.

I fit condition 5.