I do not know how much experience you have with genealogy, so please do not take offense as I try to explain the process.
Start with your parents, listing all of their information and all of their children's information. If there are any gaps in the information, contact someone (a relative) who can give you the missing information. Next you will do your parent's parents, listing all of their information and that of their children. After you have all of this information, it is time to move back another generation to your great grandparents.
We always start with the known, the present, and work backward, proving each connection as we go.
There are hundreds, if not thousands, of websites specifically for genealogy and family history research. Start with www.rootsweb.com or www.cyndislist.com, or just do a Google search for genealogy or family history websites.
I am attaching a web address so you can download free, blank, Family Group Sheets. This way you will know what information you need for each individual. You will want to make several copies.
The person in the following transcript may or may not be related to you. The name is XXXXX XXXXX to the one mentioned in your question.
New York, Passenger Lists, 1820-1957
Name: Olga Del Zotto
Arrival Date: 2 Jun 1955
Place of Origin: Michg
Port of Departure: Genoa, Italy
Port of Arrival: New York, New York
Ship Name: Constitution
I wish you luck with your search,