We usually begin with what we know using that to find later records like census, military records, naturalizations, and ship manifests. These will provide more information (dates, etc) that can help us to identify the EXACT town of birth in Italy.
Civil registrations are held at the Comune(town) level in Italy.
There are several resources you can use: A wonderful (free) site is https://familysearch.org/ for which you will need to register. You can also look at the microfilmed records from the LDS Family History Library once you know the town of record. To find the nearest Family History Library http://familysearch.org/eng/ To locate ship manifests for immigrants arriving in New York, you can use the free site http://ellisisland.org/ (you will need to register) You can also subscribe, for a fee, to sites like Ancestry.com and Fold3.com
Can we help you? If you provide some names, dates of birth, place of residence in US and possible year of immigration maybe we can get you started...