Ci siamo divertiti molto.

Because the verb here is divertirsi, which is a reflexive verb.
The ci means ourselves or, more naturally in English, it shows that we had fun.

So:

• divertire = to amuse someone
• divertirsi = to have fun, to enjoy oneself

In Ci siamo divertiti molto, ci is the reflexive pronoun for we.

The dictionary form is divertirsi.

A learner may notice that divertiti looks quite different from the infinitive, but it is just the past participle of divertirsi:

• infinitive: divertirsi
• past participle: divertito

In the sentence, it becomes divertiti because it agrees with we and the speakers are masculine or mixed gender.

Because divertirsi is a reflexive verb, and reflexive verbs normally use essere in the passato prossimo.

So the pattern is:

• mi sono divertito/a
• ti sei divertito/a
• si è divertito/a
• ci siamo divertiti/e
• vi siete divertiti/e
• si sono divertiti/e

That is why you say Ci siamo divertiti molto, not Ci abbiamo divertiti molto.

Because with essere, the past participle usually agrees with the subject in gender and number.

Here the subject is we, so the form changes depending on who we refers to:

• Ci siamo divertiti = masculine plural, or a mixed group
• Ci siamo divertite = feminine plural

If one person is speaking:

• Mi sono divertito = a male speaker
• Mi sono divertita = a female speaker

So divertiti matches a plural we that is masculine or mixed.

Yes, but only partly in the way English learners usually think about reflexive verbs.

Literally, it is something like to amuse oneself, but in normal Italian it simply means:

• to have fun
• to enjoy oneself

So you do not usually need to translate the reflexive part word-for-word.
It is best to learn divertirsi as one complete verb.

Normally, no. With divertirsi, the reflexive pronoun is part of the verb and should be included.

So the natural sentence is:

• Ci siamo divertiti molto.

Without ci, the sentence sounds incomplete or wrong for this meaning.

Molto means a lot or very much here.

It modifies the whole idea of having fun:

• Ci siamo divertiti molto = We had a lot of fun / We enjoyed ourselves very much.

Its position after the past participle is very natural in Italian.

The reflexive pronoun, the auxiliary, and sometimes the participle all change.

Examples:

• Mi sono divertito / divertita = I had fun
• Ti sei divertito / divertita = You had fun
• Si è divertito / divertita = He/She had fun
• Ci siamo divertiti / divertite = We had fun
• Vi siete divertiti / divertite = You all had fun
• Si sono divertiti / divertite = They had fun

So the sentence you have is just the we form.

The present tense is:

• Ci divertiamo molto.

That means We have a lot of fun or We enjoy ourselves a lot.

Compare:

• Ci divertiamo molto = present, habitual or current
• Ci siamo divertiti molto = past, completed event

A simple pronunciation guide is:

chee see-AH-mo dee-ver-TEE-tee MOL-toh

A few helpful notes:

• ci here sounds like chee
• siamo has the stress on sia
• divertiti has the stress on ti
• molto has a clear l, unlike in English talk

It is neutral and completely normal in everyday Italian.

It can be used in conversation, messages, and most general situations.
It is not especially formal or informal.

For example, after a trip, party, or dinner, saying Ci siamo divertiti molto sounds natural and idiomatic.