Ég las bók í gærkvöldi.

Lesa is the infinitive form, meaning to read.
Las is the past tense form, so it means read in the sense of I read / I was reading in the past.

The verb is:

• lesa = to read
• ég las = I read

This is not a regular-looking past tense from an English point of view, because lesa is a strong verb, so its vowel changes in the past tense.

You normally need ég here.

In this sentence, las is the past singular form, but it is not uniquely marked for I alone — the same form is also used with he/she/it:

• ég las = I read
• hann las = he read
• hún las = she read

So ég is what makes it clearly I.

Icelandic does not have an independent indefinite article like English a/an.

So:

• bók can mean a book or just book, depending on context.

In this sentence, Ég las bók í gærkvöldi, the natural English translation is I read a book last night.

It actually is in the correct object case: accusative.

The verb lesa normally takes a direct object in the accusative, so bók here is accusative singular. The reason you do not see a change is that for this noun, the nominative and accusative singular happen to look the same:

• nominative: bók
• accusative: bók

So the case is there grammatically, but it is not visible in the spelling of this particular form.

You would use the definite article suffix attached to the noun.

So:

• bók = a book
• bókina = the book

That gives:

• Ég las bókina í gærkvöldi = I read the book last night

This is a very important feature of Icelandic: the definite article is usually attached to the end of the noun instead of being a separate word like English the.

Í gærkvöldi means yesterday evening or last night, depending on context.

In everyday English, this sentence is often translated as:

• I read a book last night

But a more literal sense is closer to:

• I read a book yesterday evening

Here í is part of a common time expression. Literally, it is the preposition in, but in this phrase you should mostly learn í gærkvöldi as a set expression meaning last night / yesterday evening.

So even though í often means in, you should not translate the whole phrase word-for-word too mechanically. The whole expression functions as a time adverbial.

Gærkvöldi is related to gærkvöld, a compound built from:

• gær = yesterday
• kvöld = evening

In the phrase í gærkvöldi, the word appears in the dative singular form gærkvöldi, because í often takes the dative when it expresses location or time in a fixed expression like this.

So a learner can think of it as:

• base idea: yesterday evening
• actual phrase used: í gærkvöldi

Yes. Icelandic word order is flexible, but in main clauses it usually follows the verb-second rule.

The original sentence:

• Ég las bók í gærkvöldi

You can also put the time expression first:

• Í gærkvöldi las ég bók

That is still natural Icelandic. Notice that when í gærkvöldi moves to the front, the finite verb las stays in the second position, and ég comes after it.

Sometimes the simple past can cover that idea in context, but if you want to make the ongoing action clearer, Icelandic often uses vera að + infinitive:

• Ég var að lesa bók í gærkvöldi = I was reading a book last night

So:

• Ég las bók í gærkvöldi usually sounds more like a simple past statement: I read a book last night
• Ég var að lesa bók í gærkvöldi more clearly emphasizes the ongoing activity: I was reading a book last night