The index that was provided at Family Search was so you could order the appropriate microfilm from your local Family History Center (Morman Church, but all don't have FHC). The films are about $3.00 each to order. They will be microfilm copies of the actual records. You can not get a xerox copy of a record from Italy, their law does not allow it.
I recommend the book Italin Genealogical Records by Tafford Cole. It is a great reference on Italian research. There are also examples of birth, marriage and death documents and their translations. I have learned so much from this book.
If you are trying to find relatives currently living in Italy, look through other posts on this site. Your will find the link for the Italian phone book and can search for your surname in the appropriate town. You can then write to any of the folks with your surname.
Deb gave you good information. There are no records on line, only listings at the Family History Library of microfilmed records. You have to go to the library nearest your home to rent the microfilms. You can write to Italy and request the information from them, but it takes time and you will gain more out of the civil records. Here is the link you need:
It might be good to get a letter written to all ...a form letter basically...and send it to a number of people at those addresses and see what comes back. Include your e-mail address. Best to get it in Italian if possible.
You have started on a journey and you will be thrilled with what you find...but it will take time to get where you need to go. The records are in Italian and Deb mentioned the book by Trafford Cole...Italian Genealogical Records... which is wonderful...there is another book by Lynn Nelson that has a lot of info as well. It is called Discovering Your Italian Ancestors. Either one...and I have both...will help read the records. The hardest part if the late 19th century handwriting script. If you can make out the letters, a dictionary will help with the rest.
It takes about 2-3 weeks for the films to show up at your FHL branch, and then you have a month to vieiw them. They can be renewed...and after that, one more renewal will keep they in your branch on permanent loan until you release them... a good deal all around.