Barnið byrjar að öskra þegar það finnur ekki dúkkuna sína.

Barn means child as a dictionary form.
Barnið means the child.

Icelandic usually adds the definite article to the end of the noun instead of using a separate word like the.

• barn = child
• barnið = the child

So Barnið byrjar... means The child begins...

Because barn is a neuter noun in Icelandic.

Icelandic pronouns often agree with the grammatical gender of the noun, not necessarily the natural gender of the person. Since barn is neuter, it is referred to as það.

So in this sentence:

• barnið = the child
• það = it / the child

In natural English, we might say he or she if we know the child’s gender, but Icelandic often uses það with barn.

Byrja að means to begin/start to do something.

So:

• byrjar = begins / starts
• að öskra = to scream

Together:

• byrjar að öskra = starts to scream

The word að is the normal infinitive marker, like English to in to scream.

Because after byrjar að, Icelandic uses the infinitive.

• að öskra = to scream
• öskrar = screams / is screaming

So:

• barnið öskrar = the child screams
• barnið byrjar að öskra = the child starts to scream

This is very similar to English: starts to scream, not starts screams.

Þegar means when here.

So:

• þegar það finnur ekki dúkkuna sína = when it does not find its doll

It introduces a time clause, just like when in English.

In a simple Icelandic clause, ekki usually comes after the finite verb.

So:

• það finnur ekki... = it does not find...

Compare:

• Ég skil ekki. = I do not understand.
• Hann kemur ekki. = He is not coming / He does not come.

This placement is very normal in Icelandic.

Dúkka is the basic form meaning doll.
Dúkkuna means the doll and is also in the accusative singular.

It has this form because it is the direct object of finnur (finds).

So:

• dúkka = doll
• dúkkan = the doll (nominative)
• dúkkuna = the doll (accusative)

In this sentence, the child is finding or not finding the doll, so the accusative is needed.

Sinn / sín / sitt is a reflexive possessive. It is used when the possessor is the subject of the same clause.

Here, the subject of the clause is það (the child), and the doll belongs to that same child. So Icelandic uses the reflexive form:

• dúkkuna sína = its own doll

This shows that the doll belongs to the child who is doing the finding.

If you used hennar, hans, or þess, that would usually mean someone else’s doll, not the subject’s own.

A useful contrast:

• Barnið finnur dúkkuna sína. = The child finds its own doll.
• Barnið finnur dúkkuna hennar. = The child finds her doll.

Because sinn changes form to match the noun it goes with.

It agrees with dúkkuna, which is:

• feminine
• singular
• accusative

So the correct form is sína.

The pattern is roughly:

• sinn = masculine
• sína = feminine
• sitt = neuter

In this sentence, since dúkka is feminine and the object is accusative singular, sína is the right choice.

Because þegar það finnur ekki dúkkuna sína is a subordinate clause introduced by þegar.

In main clauses, Icelandic often follows verb-second word order. But in subordinate clauses introduced by words like þegar, að, ef, sem, etc., the word order is usually more straightforward:

• þegar það finnur ekki dúkkuna sína

That is, the subject það comes before the verb finnur.

Yes, finnur is the present tense of finna (to find).

The whole sentence is in the present tense:

• Barnið byrjar...
• það finnur...

Like in English, the present tense can describe:

1. something happening right now in a story or scene
2. something that generally happens

So this could mean either:

• The child starts screaming when it can’t find its doll
  or
• The child is starting to scream because it can’t find its doll, depending on context.

Yes, it could, but using það is more natural because it avoids repetition.

So you could theoretically say:

• Barnið byrjar að öskra þegar barnið finnur ekki dúkkuna sína.

But that sounds repetitive, just like saying:

• The child starts to scream when the child cannot find its doll.

Using það is the normal and natural way to refer back to barnið.

Yes—this sentence is a very useful model for several common Icelandic patterns:

1. Definite noun with suffixed article

   • barnið = the child
   • dúkkuna = the doll

2. Begin/start + infinitive

   • byrjar að öskra = starts to scream

3. Subordinate clause with þegar

   • þegar það finnur ekki... = when it does not find...

4. Negation with ekki

   • finnur ekki = does not find

5. Reflexive possession

   • dúkkuna sína = its own doll

So it is a compact sentence, but it shows several very common Icelandic grammar features all at once.