What prefix numbers are required for dialing an Italian number using a US phone with international calling setup?
Dial as you would from the U.S. +39, then the city code, then the number.
You can use “00” if your phone does not have the “+”.
Telephonically speaking, your phone is in a bubble of US territory. You keep your US number, people dial you the same way as before (how are they to know you are in Italy). You dial everything as if it was an international call:
+ {country code} { area code} {number}, as normal.
https://www.ricksteves.com/travel-tips/phones-tech/call-uk-europe
FYI, on a cell phone, hold down the 0 (zero) to get a + .