Þegar himininn er skýlaus, sjáum við fleiri stjörnur.

Þegar means when here and introduces a subordinate clause: Þegar himininn er skýlaus = When the sky is cloudless.

It tells you the time or condition under which the main clause is true.

The base noun is himinn = sky or heaven.

himininn is the definite form, meaning the sky. In Icelandic, the definite article is usually attached to the end of the noun rather than written as a separate word.

• himinn = sky
• himininn = the sky

In this sentence, himininn is also the subject of the subordinate clause, so it is in the nominative singular.

skýlaus means cloudless. It is made from:

• ský = cloud
• -laus = without, -less

So literally it means without clouds.

Here it is a predicate adjective after er (is), and it agrees with himininn in gender, number, and case.

Since himininn is:

• masculine
• singular
• nominative

the adjective appears as skýlaus, which is the correct masculine singular nominative form.

er is the present tense, 3rd person singular form of að vera = to be.

It is used because the subject is himininn (the sky), which is singular.

So:

• himininn er skýlaus = the sky is cloudless

This is a very common Icelandic word-order pattern.

Icelandic is a V2 language in main clauses, which means the finite verb usually comes in the second position.

Since the sentence begins with the subordinate clause Þegar himininn er skýlaus, that whole clause takes the first position. So the main clause must begin with the finite verb:

• Þegar himininn er skýlaus, sjáum við fleiri stjörnur.

If you said the main clause by itself, it would normally be:

• Við sjáum fleiri stjörnur. = We see more stars.

So the fronted Þegar-clause causes the inversion sjáum við.

sjáum is the present tense 1st person plural form of að sjá = to see.

That means it corresponds to we see.

So:

• ég sé = I see
• við sjáum = we see

The ending -um is one of the clues that the subject is we.

Even though the verb ending shows the person and number, Icelandic normally still uses the subject pronoun.

So sjáum already points to we, but við is still normally stated:

• sjáum við = we see

This is different from some languages where the pronoun is often dropped. In standard Icelandic, keeping við is normal.

fleiri means more when talking about countable things.

Since stjörnur means stars, and stars are countable, Icelandic uses fleiri:

• fleiri stjörnur = more stars

This is the comparative form related to margir (many).

A useful contrast:

• fleiri = more, with countable nouns
• meira / meiri = more, often for amount, degree, or uncountable things

So fleiri stjörnur is exactly what you want here.

Here stjörnur is the direct object of sjáum, so it is in the accusative plural.

The noun is stjarna = star.

Its plural form stjörnur can look the same in both the nominative and accusative plural, so the form itself does not obviously change here. But grammatically, in this sentence, it functions as the accusative object because it is what we see.

Yes. In Icelandic, a comma is commonly used after an introductory subordinate clause, especially when it comes before the main clause.

So this is standard:

• Þegar himininn er skýlaus, sjáum við fleiri stjörnur.

The comma helps mark the boundary between:

1. the subordinate clause
2. the main clause

Yes:

• Við sjáum fleiri stjörnur þegar himininn er skýlaus.

This is also correct.

The main difference is word order:

• With the main clause first: Við sjáum
• With the subordinate clause first: sjáum við

That change happens because of the Icelandic V2 rule in the main clause.

Often yes, but not always in exactly the same way in English. Its basic function is to introduce a time clause, usually when.

Depending on context, it can sometimes feel like:

• when
• whenever
• once

But in this sentence, when is the natural match.