Researching your family's history is a fascinating journey; it's like a treasure hunt! Sifting through census data, marriage and birth records, immigration records, and more -- is addicting! Just to get you started, here are a few recommendations. (However, the first step in genealogy work is to talk with your very oldest family members! Oh, the stories you will hear!)
This is an incredible resource! It costs money to use, but to start, you have the option to subscribe for just one month. Better yet, your local library provides free access!
This is the next best resource! This website is managed by the Church of Jesus Christ of Latter-day Saints. They have been conducting terrific research for a very long time. Some of the information that they provide is not available on Ancestry.com. They have recently changed their website. It is still free! And if you find records that are not readily available online, you can order the microfilm from one of their many locations for a very modest fee. They have many Faeto's civil records on-line going back to the early 1800s. Records earlier than that are kept in the town of Troia. Looking at records in Troia will require an actual visit to Italy:-)
Here is a great link to a list of helpful information for Italian (and Faeto-related) genealogy research.
Here is a link to Cleveland genealogy information.
Here is a link to a sampling of civil records from Faeto!
Now if you really get the genealogy bug, consider DNA testing.
FamilyTreeDNA is highly recommended. The first set of 12 markers will give you only very ancient information --- we all originated somewhere in Africa and some migrated to Europe and some migrated to Asia. That is about all you'll find out with the basic test. You have to order additional markers to increase the odds of learning more about the migration pattern of your line. If you are one of the lucky ones with a very popular name that has alot of people who have submitted their DNA, you might find important connections with others who can help you understand your roots. HOWEVER - please, please, please do the autosomal test. In FamilyTreeDNA it's called "Family Finder". The other DNA platforms have the autosomal test too, but each of them have their own name for that test. IMPORTANT: after you have your autosomal test results, upload them to gedmatch.com It's free and easy and very valuable for finding connections.