Fólkið á safninu talar hljóðlátt.

Because fólk in Icelandic is a collective noun. Grammatically, it is singular and neuter, but in English we usually translate it with the plural word people.

So:

• fólk = people
• fólkið = the people

Even though the meaning is plural in English, Icelandic treats it as a singular noun in grammar.

Because the subject fólkið is grammatically singular.

• tala = to speak
• talar = speaks / is speaking

So Icelandic uses the 3rd person singular verb form with fólkið:

• Fólkið talar = the people speak

This feels unusual to English speakers, because English uses a plural verb with people, but Icelandic is following the grammar of fólk, not the English translation.

In this sentence, the most natural reading is that á safninu goes with fólkið:

• Fólkið á safninu = the people at the museum

So the subject is really the whole phrase Fólkið á safninu, and then:

• talar hljóðlátt = speaks quietly

This also helps explain the word order. The verb comes after that whole subject phrase.

Because á takes different cases depending on meaning:

• dative for location: being somewhere
• accusative for movement toward somewhere

Here the meaning is location, so Icelandic uses the dative:

• á safninu = at the museum

Compare:

• á safnið = to the museum
• fara á safnið = to go to the museum

So the ending in safninu shows that this is a location phrase, not a motion phrase.

Icelandic usually puts the at the end of the noun instead of using a separate word.

Here you can see it in two places:

• fólkið = fólk
  • definite ending = the people
• safninu = safn in the dative definite form = the museum

So Icelandic often says the by changing the noun itself, not by adding a separate word like English the.

It is an adjective form, but Icelandic often uses the neuter singular form of an adjective adverbially.

The adjective is:

• hljóðlátur (masculine)
• hljóðlát (feminine)
• hljóðlátt (neuter)

After a verb like talar, the neuter form hljóðlátt means something like:

• quietly
• in a quiet way

So:

• talar hljóðlátt = speaks quietly

This is very common in Icelandic.

Usually the best general translation is at the museum, but in some contexts English might also say in the museum.

Icelandic á is often used where English prefers at, especially with places and institutions. So á safninu is a normal way to say someone is at the museum.

If you want to emphasize being physically inside the building, Icelandic may also use í in some contexts, but in your sentence á safninu is the idiomatic form given.

Here is a word-by-word breakdown:

• Fólkið

  • from fólk
  • neuter singular definite
  • subject of the sentence

• á

  • preposition
  • here it means at
  • with location, it takes the dative

• safninu

  • from safn = museum
  • dative singular definite
  • part of the phrase á safninu

• talar

  • present tense of að tala
  • 3rd person singular
  • speaks / is speaking

• hljóðlátt

  • neuter singular form of hljóðlátur
  • used adverbially here
  • quietly

So the structure is:

• [Fólkið á safninu] [talar] [hljóðlátt]
• [The people at the museum] [speak] [quietly]