Decidono di divorziare.

Decidono is the third-person plural form of decidere in the present indicative.

• io decido = I decide
• tu decidi = you decide
• lui/lei decide = he/she decides
• loro decidono = they decide

So decidono means they decide.

Italian often leaves out subject pronouns when the verb ending already makes the subject clear. Since -ono shows this is loro (they), you do not need to say loro.

So:

• Decidono di divorziare. = They decide to get divorced.
• Loro decidono di divorziare. = also correct, but more emphatic, as if you want to stress they.

It is the present indicative.

In a simple sentence like this, it usually means they decide or, depending on context, sometimes they are deciding in a broad sense. In storytelling, the Italian present can also be used where English might use the past, but by itself this form is just the normal present tense.

Because decidere is commonly followed by di + infinitive when you say what someone decides to do.

Pattern:

• decidere di + infinitive

Examples:

• Decido di partire. = I decide to leave.
• Abbiamo deciso di aspettare. = We decided to wait.
• Decidono di divorziare. = They decide to get divorced.

This is just the normal construction of the verb.

Because after decidere di, Italian uses the infinitive.

So the structure is:

• decidono = they decide
• di divorziare = to get divorced

This works like English to + verb:

• They decide to leave
• They decide to divorce / get divorced

In this kind of sentence, divorziare usually means to get divorced.

So Decidono di divorziare is most naturally understood as:

• They decide to get divorced

Even though English often says get divorced, Italian simply uses the verb divorziare.

No. After decidere, the normal construction is di + infinitive, not a + infinitive.

So:

• decidono di divorziare = correct
• decidono a divorziare = incorrect

Different Italian verbs take different prepositions before an infinitive, so this is something you often have to learn verb by verb.

Normally, if the subject is the same, Italian prefers decidere di + infinitive:

• Decidono di divorziare.

A che clause is possible in some contexts, but it is less natural here. Very often, che is used when the second clause has a different subject, for example:

• Decidono che i figli resteranno con la madre.
  = They decide that the children will stay with the mother.

So for this sentence, di + infinitive is the standard choice.

Yes, divorziare is a regular -are verb.

Its infinitive is divorziare, and forms are built like other regular -are verbs, for example:

• divorzio = I get divorced
• divorzi = you get divorced
• divorzia = he/she gets divorced
• divorziamo = we get divorced
• divorziate = you all get divorced
• divorziano = they get divorced

In your sentence, though, it stays in the infinitive because it follows di after decidono.

A simple approximate pronunciation is:

deh-CHEE-doh-no dee dee-vor-TSYAH-reh

A few helpful points:

• ci in decidono sounds like chee
• di is pronounced dee
• z in divorziare here sounds like ts
• the final -re in the infinitive is pronounced, not silent

A more IPA-style version would be roughly: /deˈtʃidono di divorˈtsjare/

The basic meaning is the same, but loro adds emphasis or contrast.

• Decidono di divorziare. = neutral, natural
• Loro decidono di divorziare. = they decide to get divorced, perhaps contrasting them with someone else

Italian usually prefers the version without the pronoun unless there is a reason to stress it.