Polite 'lei' and why it uses third-person forms
When Italians speak politely to one person, such as a shop assistant, a hotel receptionist or an older stranger, they do not use tu. They use Lei, a pronoun that is grammatically third person and looks exactly like the word for she. With it come third-person verbs (Lei è, not tu sei), third-person commands (scusi, mi scusi), the possessive suo for your, and even goodbyes like arrivederla.
English speakers trip over this because English has a single you for everyone. Speaking to someone as if they were she feels strange at first, especially when that someone is a man. Once you see that all these words share the same logic, though, polite Italian becomes very predictable.
Think of Lei as a respectful way of saying you, with the grammar of he or she. Every verb that goes with it takes the same form you would use for one other person: Lei ha (you have), Lei sa (you know), Lei è (you are). Because Italian verbs already show the person, the pronoun itself is often left out: Ha una prenotazione? means the same as Lei ha una prenotazione?
The grammar is third person, but adjectives describing the person follow their real sex. To a man you say Lei è stanco, with masculine stanco, even though Lei looks feminine.
Scusi and mi scusi are third-person command forms: literally something like may you excuse (me). Use them to get a stranger's attention or to apologise to one person you do not know well. The informal versions are scusa and scusami. Other everyday polite commands work the same way, like senta (listen, excuse me) and si accomodi (have a seat, come in).
Suo is the possessive that goes with Lei. Like all Italian possessives, it agrees with the thing owned, not with the owner: suo passaporto, sua valigia, suoi documenti, sue chiavi. So a man is asked about sua moglie, with feminine sua, because moglie is feminine.
On its own, suo means yours. The article is often dropped after essere.
Arrivederla is arrivederci with the polite object pronoun La attached: roughly until I see you again. Use it when leaving one person you address with Lei.
The typical mistake is starting politely and slipping into tu forms: Scusi, sei italiano? Keep everything third person: Scusi, è italiano?
Writing Lei and Suo with a capital is a courtesy that is common in letters and emails, but it is optional. Many people simply write lei and suo.
Lei can also mean she, and suo can mean his or her. Context and tone of voice almost always make the meaning clear.
The very formal plural Loro exists, but today Italians normally address a group with voi, even politely.
When you speak politely to one person, talk to them as if they were he or she: third-person verbs with Lei, third-person commands like scusi and mi scusi, suo for your and yours, and arrivederla to say goodbye. Adjectives still match the person's real sex, and suo matches the thing owned.