Kennarinn fær okkur til að skrifa sömu sögn fyrst í nútíð og svo aftur í framtíð.

This is a very common Icelandic pattern:

fá + object + til að + infinitive

It means to get/make someone do something.

So:

• Kennarinn fær okkur til að skrifa ...
• literally: The teacher gets us to write ...

Here, fær is the present tense of fá.
On its own, fá can mean things like get, receive, or obtain, but in this construction it means get someone to do something.

Because -inn is the suffixed definite article in Icelandic.

• kennari = a teacher
• kennarinn = the teacher

So Kennarinn means the teacher. It is also in the nominative singular because it is the subject of the sentence.

Because við is the subject form (we), but here the meaning is us, not we.

Compare:

• við = we (nominative)
• okkur = us (object form)

In this sentence, the teacher is getting us to do something, so Icelandic uses okkur.

In the pattern fá einhvern til að gera eitthvað, the person being made/gotten to do something is the object.

Here til að introduces the infinitive phrase after fá.

• að skrifa = to write
• til að skrifa = part of the construction fá einhvern til að skrifa

So in this sentence, til að is not just a loose in order to. It is part of the fixed pattern:

• fá einhvern til að gera eitthvað
• get someone to do something

You will see til að elsewhere with a more direct meaning of in order to, but here it belongs to this verb pattern.

Because sami (same) is irregular, and its form changes to match gender, number, and case.

Here:

• sögn is feminine singular
• it is the object of skrifa
• so sami has to appear in the matching form

That matching form is sömu.

So:

• sömu sögn = the same verb

This is one of those forms that learners usually just need to get used to, because sami does not behave like a completely regular adjective.

It is in the accusative, because it is the direct object of skrifa.

The structure is:

• skrifa = write
• skrifa sögn = write a verb

The reason sögn does not visibly change is that many Icelandic feminine nouns have the same form in nominative and accusative singular.

So even though the case is accusative, the word still looks like sögn.

They organize the sequence of the task:

• fyrst = first
• svo = then
• aftur = again

So:

• fyrst í nútíð = first in the present tense
• og svo aftur í framtíð = and then again in the future

The word aftur makes it clear that the students are writing the verb a second time, not just moving on to a new idea.

Because Icelandic often uses í with names of tenses or grammatical forms.

So:

• í nútíð = in the present tense
• í framtíð = in the future tense

This works much like English in the present tense.

Here:

• nútíð = present tense / present time
• framtíð = future tense / future time

So the sentence is telling the learner which tense to use when writing the verb.

This is a good question, because the answer is not quite in the same way as some other languages.

Icelandic does not usually have a single special verb ending that functions as a straightforward future tense. Future meaning is often expressed with:

• the present tense
• munu
• sometimes ætla að
• other context-based ways

But in teaching and grammar explanations, framtíð is still a normal and useful label. So in a classroom sentence like this, í framtíð is perfectly natural.

In other words, the sentence is talking about writing the verb in a future-time form or future construction.

Because Icelandic, like English, often avoids repeating words that are already understood.

The full idea is:

• write the same verb first in the present tense
• and then write it again in the future

After skrifa sömu sögn has already been said once, Icelandic can simply add:

• fyrst í nútíð og svo aftur í framtíð

The second skrifa is understood from the first part.

The word order here is natural and straightforward:

• Kennarinn = subject
• fær = verb
• okkur = object
• til að skrifa = infinitive phrase
• sömu sögn = object of skrifa
• fyrst í nútíð og svo aftur í framtíð = adverbial information about how/when to write it

So the sentence is built in a very normal Icelandic way.

Icelandic word order can be flexible, but this version is the neutral, classroom-style order a learner would expect to see.