When someone answers the phone, they’ll say “pronto,” which actually means “ready.” This dates from the days when you probably did have to be ready to receive the call. Now it’s simply the equivalent of “hello” on the phone.
When we’re in an official or business situation where two speakers might not know each other, there’s a formula for what to say after that. In America, if you call a business, they might say, “How can I help you?” or “What can I do for you?” Or more coldly, “Yes?”
In Italy, the verb dire (to say, to tell) is what’s used, conventionally.
Pronto? Commissariato, dica pure.
Hello, police headquarters, go ahead, tell me [I'm listening].
Caption 27, Il Commissario Manara - S1EP9 - Morte in paradiso - Part 4 Play Caption
In the above example, Quattroni adds pure (also). He’s being extra polite and saying, “Go ahead and state your business. [You’re not disturbing me, I’m listening].” Pure is a great adverb to sprinkle into the conversation. Please see the Yabla lesson on pure!
While pronto is used exclusively on the phone, dica is also used in person when you go to the counter at the post office, or some other kind of office. The person who says dica, or mi dica, is essentially asking you (politely) to state your business.
In the following example, Massimo works for Doctor Nicasto. So when he says dica, he is most likely asking for instructions or information.
Massimo. -Ah, dica, dottor Nicasto, dica.
Massimo. -Ah, what can I do for you, Doctor Nicasto, what can I do for you?
Caption 59, Il Commissario Manara - S1EP5 - Il Raggio Verde - Part 4 Play Caption
Grammatically speaking, dica is the formal second person singular imperative of the verb dire. It’s worth mentioning that in Italian, the formal imperative is actually taken from the third person singular subjunctive of dire (see chart from coniugazione.it below).