One of the most difficult genealogical tasks you may face in researching your Italian roots is in tracing the ancestry of an Italian foundling.
Known in Italy as Trovatelli or Proietti, a foundling is a child abandoned at birth, for one reason or another. The most common is that the child was born out of wedlock, but others, such as; the family being to poor to care for another child, are not unheard of.
These infants were usually left at a foundling home. The foundling homes were a place where Italian women could legally abandon their children, with complete anonymity (although, often times, especially in small towns, the identity of at least the mother was generally known). Sometimes children were left with tokens to indicate their parentage, in the event the mother or father should ever want to reclaim them, although, this was rare.
After the child was abandoned, their birth would be registered in the Stato di Civile, under a name the mayor or other town official would give the child. These names were made up by the town official, some of the names were unique (such as one I have in my ancestry, Clemanni), others were generic names given to many foundlings, such as; Esposito (literally meaning "exposed").
After the infant's birth was registered, they were placed in the care of a woman who recently had given birth to a child (usually one that had recently lost a child). These women were called, wet nurses. The roles these women had in the child's life varied greatly. Some took the child in, simply to collect money given to them by the town to care for the child, others treated them as their own, sometimes even giving the child their own surname.
Often times, family lore and myths existed about the child's parents. A common one is that the foundling was the child of a nobleman. These stories, while not always untrue, can stem from a variety of sources. One being that the mother made the claims while pregnant (to dignify to some extent something that was a social taboo at the time). Secondly being that when the child was born, he/she was given a name by the town official, that sounded "noble" (Della Luna, for instance). Whatever the case, while these stories are fun to think about, always take them with a grain of salt.
Birth records for foundlings can be found in the Registri dello Stato Civile, Atti di Nascita (birth acts) of the child's town of origin, usually in Parte II. These records rarely give the parents names (as previously stated, their identity was to be kept secret if they chose it to be).
If his or her parents recognized the child, these records can usually be found in the Atti Diversi (Misc. acts) for the year of the child's birth.
Other records that can help you in tracing your foundling ancestor's genealogy are marriage records and baptism records. Marriage records would be found in the Registri dello Stato Civile, Atti di Matrimonio (marriage acts), whereas baptism records (battesimo) are maintained by the church where he/she was baptized, and can be hard to obtain.
Again, tracing the ancestry of a foundling can be incredibly difficult, and sometimes, impossible, so to familiarize oneself with the common procedures that took place is very important. Foundling history in Italy is complex, and I couldn't begin to go through all the variables in one post. This is just an attempt to help you understand the general process. A valuable resource for further research is the book ‘Sacrificed for Honor: Italian infant abandonment and the politics of reproductive control’ by David I. Kertzer.