Nemendur verða að vera ábyrgir fyrir náminu sínu.

In this sentence, verða að means must or have to.

• verða on its own often means become
• but verða að + infinitive is a fixed pattern meaning must / have to

So:

• Nemendur verða að vera... = Students must be...

Because verða að is followed by an infinitive.

Here, the action/state that the students must have is:

• vera ábyrgir = be responsible

So the structure is:

• Nemendur = subject
• verða að = must / have to
• vera = infinitive verb
• ábyrgir = adjective complement

Literally, it is something like:

• Students must be responsible...

Yes, very often it does.

For example:

• Hann verður þreyttur. = He becomes tired.

But when you see verða að + infinitive, it usually means must / have to instead.

So in this sentence, verða does not mean become. It is part of the expression verða að.

Because it agrees with nemendur.

• nemendur = students = plural
• ábyrgir = plural form of ábyrgur = responsible

After vera, Icelandic adjectives normally agree with the subject in gender, number, and case.

So:

• singular: Nemandi verður að vera ábyrgur.
• plural: Nemendur verða að vera ábyrgir.

Because ábyrgir is a predicate adjective linked to the subject through vera, so it matches the subject:

• nemendur = nominative plural
• ábyrgir = nominative plural

The dative belongs only to the prepositional phrase:

• fyrir náminu sínu

So the sentence has:

• subject + predicate adjective in nominative
• preposition + object in dative

Because ábyrgur fyrir is the normal Icelandic way to say responsible for.

This is a common combination:

• vera ábyrgur fyrir einhverju = to be responsible for something

So you should learn ábyrgur together with fyrir, not as two completely separate choices.

Because fyrir here takes the dative, and the noun is in the definite singular.

The noun is:

• nám = study, learning, education
  (neuter noun)

Its relevant forms are:

• nám = nominative/accusative singular, indefinite
• námið = nominative/accusative singular, definite
• námi = dative singular, indefinite
• náminu = dative singular, definite

Since the sentence has fyrir + dative, you get:

• fyrir náminu

sínu is a reflexive possessive form, from sinn / sín / sitt.

It means something like:

• his own
• her own
• their own

Here it refers back to the subject nemendur.

So:

• náminu sínu = their own studies / their own learning

This is very common in Icelandic when the possessor is the subject of the same clause.

Because sinn agrees with the thing possessed, not with the possessor.

The possessed noun here is náminu, which is:

• neuter
• singular
• dative

So the matching form is:

• sínu

That is why Icelandic uses:

• náminu sínu

not:

• náminu sitt
• náminu sínir

You could say náminu þeirra, but sínu is the more natural choice here.

The difference is:

• sínu = reflexive, referring back to the subject itself
• þeirra = non-reflexive their

So:

• Nemendur verða að vera ábyrgir fyrir náminu sínu.
  = The students must be responsible for their own studies.

Using sínu makes the connection to the subject especially clear.

It is nominative plural, because it is the subject of the sentence.

The singular form is:

• nemandi = student

The plural is:

• nemendur = students

So the sentence begins with a straightforward nominative plural subject.

The sentence follows a very normal Icelandic order:

• Nemendur — subject
• verða að vera — verb chain
• ábyrgir — predicate adjective
• fyrir náminu sínu — prepositional phrase

So, in a simple breakdown:

• Students
  • must be
    • responsible
      • for their studies

This is a good example of standard, neutral Icelandic sentence structure.