You'll frequently run into the acronym "LIRA" which is last Italian registered ancestor. This is the person up your family line that was born in Italy. You'll need to find where they were born in Italy.
Italy is broken down into regions, and then communes inside of those regions. Each commune has a civil office that has been record keeping in handwritten books that go back to the 1800's! You can see some of these records online at familysearch.org for free by creating an account.
For me, it was my Great Great Grandfather, Arsenio Giordano. Born in 1887 in Sant'Arsenio, Salerno, Italy. My first clue was from Ancestry.com where I saw this military registration card that had all the great information that I needed to start.
Quick sidebar, my aunt Cheryl was doing genealogy for our family for a very long time and asked if I were interested in doing it and I said I wasn't. I started getting into it through this process and love it. If you have a family member that can help you find things, definitely hit them up!
For the Los Angeles Consulate, the documents I needed to acquire were Arsenio's Italian birth record, certificate of naturalization, marriage records, and death certificate. So, this military record was not required. But this is the stepping stone I needed for the next step, acquiring the Italian birth record.
Last Name Tools
I found this tool later in my research, but thought it would be very helpful if I didn't have the other clues I had already found. I knew my GGF was born in Sant'Arsenio, Salerno from the document above, but I wasn't sure where his mom, my GGGM was from. I knew the name was Aromando, though. I found these two tools which seem to be clearly sourced from different places, but they both seem to have great information.
1: https://www.mappadeicognomi.it This site gives you a map of Italy, you put in your cognome (last name) and it will show red circles over the areas of concentration of that last name like a heat map. In my case, Giordano which is a very common name, will show all over the place with concentrations near Venice and Napoli. While that's great, Aromando is not found.
2: https://ganino.com/cognomi_italiani_a This site I ran across is like a wiki of name origins which is super-intersting! When I look up Aromando here, it states, "Assolutamente rarissimo specifico del salernitano, sembrerebbe originario della zona che comprende Sant'Arsenio (SA) e Pietro Al Tanagro (SA), dovrebbe derivare dal termine longobardo Arimanno (uomo libero)." which translates to basically, "Absolutely very rare and specific to Salerno, seems to originate from the zone that includes Sant'Arsenio and Pietro Al Tanagro, the name is derived from the Lombard term "Arimanno" which means free man".
I haven't looked very deeply, but as it is now, I have not been able to find my GGGM birth records, but I bet they are also in Sant'Arsenio around 1867. If memory serves, those records were not available online yet, but more are being added all of the time. You may have a last name and no idea from where in Italy it is from, this might give you some pointers on where to look.