Domani ci vediamo alle sedici in biblioteca.

Here ci is a pronoun meaning each other or one another.

So ci vediamo literally means we see each other, but in natural English it often corresponds to we’ll meet or we’re seeing each other in the sense of meeting up.

This is not the ci that means there. In this sentence, it is part of the verb vedersi.

• vedere = to see
• vedersi = to see each other / to meet

So:

• Ci vediamo domani = We’ll see each other tomorrow / See you tomorrow

Italian very often uses the present tense to talk about the near future, especially when there is a clear time expression like domani.

So Domani ci vediamo is completely natural and means:

• We’re meeting tomorrow
• We’ll see each other tomorrow

English does something similar:

• I’m leaving tomorrow
• We’re meeting at four

Italian could use a future form in some contexts, but here the present is the most natural choice.

In Italian, subject pronouns like io, tu, noi, voi are often omitted because the verb ending already shows who the subject is.

Here, vediamo tells you the subject is we.

So:

• (Noi) ci vediamo = We’ll see each other

Adding noi is possible, but it is usually only used for emphasis or contrast:

• Noi ci vediamo alle sedici, loro più tardi.
  We’re meeting at 16:00; they’re meeting later.

Without emphasis, leaving it out is more natural.

Italian uses a + definite article when telling the time.

Because sedici is plural in form, you use le:

• a + le = alle

So:

• all’una = at one
• alle due = at two
• alle sedici = at sixteen hundred / at 4 p.m.

This is the normal pattern for clock times.

Italian often uses the 24-hour clock, especially in schedules, appointments, formal situations, and everyday speech.

So:

• alle sedici = at 16:00 = at 4 p.m.

You may also hear alle quattro, but that can be ambiguous unless the context makes it clear whether it is morning or afternoon.
Using alle sedici removes any doubt.

In Italian, some place expressions often appear without an article, especially when referring to the place in a general way.

So in biblioteca means:

• at the library
• in the library

It is similar to expressions like:

• a scuola = at school
• in chiesa = in church
• in ufficio = at the office / in the office

If you say nella biblioteca, it usually sounds more specific, as if you mean a particular library building or a specific library already known in the conversation.

So:

• in biblioteca = at the library, generally
• nella biblioteca comunale = in the municipal library, specifically

Not exactly literally, but that is often the best natural translation.

Literally:

• ci vediamo = we see each other

But in many real-life situations, Italians use it where English would say:

• we’re meeting
• see you
• we’ll meet

So in this sentence, ci vediamo is a very natural way to express an arranged meeting.

Yes. Italian word order is fairly flexible, and that version is also natural:

• Ci vediamo domani alle sedici in biblioteca.

The original sentence begins with Domani, which puts a little focus on tomorrow.

Very natural alternatives include:

• Domani ci vediamo alle sedici in biblioteca.
• Ci vediamo domani alle sedici in biblioteca.
• Alle sedici ci vediamo in biblioteca.

The meaning stays basically the same, but the emphasis can shift depending on what comes first.

Putting domani first helps frame the whole sentence right away in time.

It is like saying:

• Tomorrow, we’re meeting at 16:00 in the library.

Italian often puts time expressions early in the sentence, especially when they set the scene.
But it is not mandatory; it is just a very common and natural choice.

Either can work, depending on the context.

Italian in biblioteca literally uses in, so in the library is close to the form.
But in English, when talking about a meeting location, at the library is often the more natural translation.

So:

• Domani ci vediamo alle sedici in biblioteca.
  can be understood as
  Tomorrow we’re meeting at the library at 4 p.m.

If the emphasis is on being physically inside the building, in the library also works.

Not in the same way.

Ci vediamo is the natural expression here.

The verb incontrare means to meet, but incontriamo by itself means we meet / we are meeting only in certain contexts and is not the usual equivalent of this sentence.

To express the same idea with incontrare, you would more naturally say something like:

• Ci incontriamo domani alle sedici in biblioteca.

That is grammatical, but ci vediamo is more common and more conversational for arranging to meet.