A. Overview You need to know the town in Italy where your ancestors lived or were born.
If you know the town, that's fantastic! You can start searching for your ancestor's birth, marriage, and death records.
If you do not know the town and want to do your own search, look at the Search Strategies below.
If you cannot find the town after doing your own search and want me to take a look, purchase the Don't Know My Town of Origin package ($100, 4-hours).
B. Search Strategies
(1) Search at Home First See what you can find at home. Or, what other family members might have.
Look through family papers, family bible, or other memorabilia.
Contact other family members to see if they know.
(2) Search Online You should search for the documents below. It is possible one might list the town. Or, provide you with a clue for your next search. FamilySearch provides millions of online records and is free. If you have a subscription to services such as Ancestry and MyHeritage, you can start there.
Passenger Lists.
Online Family Trees on FamilySearch, Ancestry, MyHeritage, etc.
Birth Certificate, Marriage License, Death Certificate.
Naturalization Records: Declaration of Intention and Petition for Naturalization.
Be careful, sometimes a person might list "Napoli" as the town where he/she was born. Napoli [Naples] is both the name of a town and the name of a Province. You have to be careful whether the person was really born in the town of Napoli or in a town within the Province of Napoli (such as Pomigliano d'Arco for my grandparents). This is like saying I was born in North Carolina. That's just not specific enough. You need to know the specific town.
A person might also say "I'm from Campania." Again, that's not precise enough. Campania is one of the 20 Regions of Italy.
If you still can't find the town of origin for your ancestor, you might try searching records for this person's parents, siblings, or spouse. You just might find a passenger list for a brother that lists the town of birth for the brother. That would definitely be the starting place to search for your ancestor.