Not long ago, I talked about the t-v distinction, which is the most common form of formal address in most languages. Italian, however, does things a little differently.
Instead of pluralizing the second person, or adding a title (like sir), Italians abstract into the third person. In the singular, this means that they call each other “she”.
For example, when asking how someone is doing, if you are talking to someone with whom you are familiar you might say Tu, come stai? But when asking more formally, you would say Lei, come sta? Literally, you’re asking “how is She doing?” Take note, however, that whether you are speaking to a man or a woman, you always use Lei as the formal singular subject pronoun.
In the plural, things are less weird, basically because there is no gender on the plural subject pronoun. But there is still a shift from 2nd to 3rd person. For example, when asking if a group of people are hungry, you might ask Voi, avete fame? But in the formal you would now say Loro, hanno fame?
So when should the familiar form be used and when should the formal form be used? Here are some guidelines:
Using a familiar form where formal would be expected is considered disrespectful, so whenever you are in doubt, it is best to err on the side of formal.
Another style note is that English-speakers typically use “please” and “thank you” a lot as a way to show politeness, but because this can be established already by the tone of a request, such as by choice of suject pronoun, Italians use these courtesy words far more sparingly.
When people are getting to know each other, they start off on a formal footing, but after their relationship progresses, one will typically suggest Possiamo darci del tu? (Can we be familiar?) It would be rare to be refused.