The Basics of Italian citizenship
Italy offers citizenship on the basis of jure sanguinis (a Latin term for "by right of blood"). This means that a child is not an Italian citizen just by being born in Italy. Instead, a child is an Italian citizen at birth only if one of his parents is. Contrast this with the United States, which offers citizenship on a jure soli basis (Latin for "by right of soil"), and wherein a child born on U.S. soil is automatically American regardless of his parents' citizenship.
When a child is born on U.S. territory to an Italian citizen parent, that child is born with both U.S. citizenship jure soli, and Italian citizenship jure sanguinis. This means that as long as your last Italian-born ancestor was still an Italian citizen at the time his/her child was born in the U.S., the child was given both citizenships automatically at birth. Then, that Italian citizenship can pass down from generation to generation in the United States without interruption, all the way down to you!
How to qualify
There are four basic rules to qualifying.
Your Italian ancestor must have been alive--anywhere in the world--on or after March 17, 1861.
If your ancestor ever became an American citizen, it must have been both after July 1, 1912 and after the birth of his or her U.S.-born child.
If your ancestor never became a U.S. citizen, you automatically qualify. Refer to number 4 if you have any women in your direct line.
If you have any women ancestors in your direct line, the date on which they had their child determines how you apply for recognition. If the child was born before January 1, 1948, you have to go to the Court of Rome. If the child was born after, you can apply in Italy or at an Italian consulate.
Exceptions to the rules
and a loophole
When Italy became a unified nation on March 17, 1861 not all of the territory we now associate with it became a part of the country. Some Italian regions were annexed only afterward.
Therefore, if your ancestor comes from one of the below places, he or she must have still been in Italy on these dates:
Veneto: August 12, 1866
Trentino Alto Adige, Friuli Venezia Giulia, and Zara: July 16, 1920
The city of Fiume: 1924
If you have a male ancestor who lost Italian citizenship before the birth of his U.S.-born child and don't qualify through him, there may be a loophole. If that male ancestor married his U.S.-born wife prior to April 27, 1983, then she automatically became an Italian citizen upon marriage. Her Italian citizenship would survive--even if her husband lost his own--and can pass down successfully.