There are several major benefits to obtaining Italian dual citizenship. As an Italian citizen, you qualify for social services provided by the Italian government and your children are able to become Italian citizens automatically. As an added benefit, Italy's membership in the European Union allows Italian citizens---even those who live abroad or have dual citizenship---to travel, work, and live anywhere in Europe with great ease. The application process to become a dual citizen is lengthy and requires a significant time commitment.
See if you qualify
Review the qualifications to obtain dual citizenship. Generally speaking, your father, mother (unless you were born after 1947), grandfather or great-grandfather must have been an Italian citizen in order for you to claim Italian citizenship. It's also possible to obtain dual citizenship if your spouse is an Italian citizen. Several conditions apply, and you should consult with an Italian official to ensure that you qualify before beginning the application process.
Obtain the necessary documents. This can be complicated, especially if your claim to citizenship comes from a grandparent or great-grandparent. For instance, if you're staking your claim based on your father's citizenship, you'll need copies of the birth certificates for both him and his spouse, their death certificates (if applicable), your and your spouse's birth certificates, and marriage certificates for both couples. Go to http://www.italiamerica.org/id72.htm for a handy drop-down menu of the documents you'll need based on the circumstances of your application.
Go to your local consulate general. Italy has consulate general offices in many major American cities, and you can obtain citizenship applications from officials there. The process will go faster if you've already obtained the documents above, since the application also requires signatures from ancestors who are Italian citizens (or, if they're deceased, your signature on their behalf).
Fill out the citizenship application and submit it to the consulate general. Turn in the application to the same office where you obtained it.
Wait. This process is lengthy, and it can take a year or longer for Italian consular officials to get back to you. Once they do, they'll advise you of any additional steps to take before you can become an official citizen.