Depois do almoço, voltámos ao recreio e começámos a comentar o livro outra vez.

Because Portuguese normally contracts the preposition de with the masculine singular article o:

• de + o = do

So depois do almoço is the natural form.

It is also normal in Portuguese to use the article with meals in expressions like:

• antes do jantar
• depois do almoço

Even though English usually says after lunch without an article, Portuguese often uses one here.

They are in the pretérito perfeito: the normal tense for completed past actions.

• voltámos = we went back / we returned
• começámos = we started / we began

This tense is used because the sentence is telling a sequence of completed events in the past: first they went back, then they started discussing the book again.

In European Portuguese, that accent helps show both the stress and the tense.

• voltámos = past, we went back

• voltamos = present, we go back / we return

• começámos = past, we started
• começamos = present, we start

So the accent is very useful because it distinguishes the past form from the present one.

Because Portuguese often drops subject pronouns when the verb ending already shows who the subject is.

Here, the ending -mos tells you the subject is we:

• voltámos
• começámos

So nós is not necessary. You could say nós voltámos..., but that would usually add emphasis or contrast.

Because ao is a contraction of:

• a + o = ao

Here it means something like to the playground / back to recess.

With verbs of movement or return, Portuguese often uses a before the destination:

• voltar ao recreio
• ir à escola
• chegar ao parque

So ao recreio is the normal contracted form.

In a school context in Portugal, recreio can mean:

• the playground / school yard
• the recess / break time

In this sentence, ao recreio most naturally sounds like back to the playground/school yard, but depending on context it can also carry the idea of going back out for recess.

Because começar is normally followed by a + infinitive when you mean to start doing something.

So:

• começar a comentar = to start commenting / to start discussing
• começar a ler = to start reading
• começar a falar = to start speaking

So começámos a comentar o livro is the standard structure.
You would not normally say começámos comentar.

Because in Portuguese, comentar is usually a direct transitive verb. It normally takes a direct object with no preposition:

• comentar o livro
• comentar o filme
• comentar a notícia

English often uses comment on, but Portuguese usually just says comentar + noun.

So comentar o livro is perfectly natural.

Outra vez means again or once more.

In this sentence, it most naturally refers to the idea of discussing the book again:

• começámos a comentar o livro outra vez = we started discussing the book again

It is very common in everyday Portuguese. Alternatives like de novo or novamente are also possible, but outra vez is especially common in speech.

Because depois do almoço is an introductory time phrase, and putting a comma after it is very natural.

It works like English:

• After lunch, we went back...

The comma helps separate the time setting from the main action. In very short sentences, people sometimes omit this comma, but here it is completely standard and reads smoothly.