Á morgun sýnir kennarinn hvernig sögnin lítur út í framtíð.

Because Icelandic is a V2 language in main clauses. That means the finite verb normally comes in the second position.

Here, Á morgun is placed first for emphasis or simply because it is the time expression. Once that takes the first slot, the verb must come next:

• Á morgun — first position
• sýnir — second position
• kennarinn — subject

So this word order is completely normal in Icelandic.

If you started with the subject instead, you could also say:

• Kennarinn sýnir á morgun ...

Both are fine, but the sentence you have emphasizes tomorrow first.

Icelandic often uses the present tense to talk about the future when the time is already clear from the context.

So:

• Á morgun sýnir kennarinn ...

can naturally mean:

• Tomorrow the teacher will show ...

This works much like English sentences such as:

• Tomorrow I leave early.
• Next week we start school.

The word Á morgun already makes the future meaning clear, so Icelandic does not need a separate future tense form here.

The ending -inn is the definite article attached to the noun. Icelandic usually adds the to the end of the word instead of putting a separate word in front.

So:

• kennari = teacher
• kennarinn = the teacher

In this sentence, kennarinn is the subject, so it is in the nominative singular definite form.

For the same reason as kennarinn: the ending -in marks the noun as definite.

• sögn = verb
• sögnin = the verb

So sögnin means the verb, not just a verb.

This is the subject of the embedded clause:

• hvernig sögnin lítur út ...
• how the verb looks ...

Hvernig means how and introduces an indirect question or embedded clause.

So:

• hvernig sögnin lítur út literally means
• how the verb looks

This is similar to English in sentences like:

• The teacher shows how the verb looks.

So the whole sentence structure is:

• main clause: Á morgun sýnir kennarinn ...
• embedded clause: hvernig sögnin lítur út í framtíð

Because this is a subordinate clause, not a main clause.

In the main clause, Icelandic follows V2 word order:

• Á morgun sýnir kennarinn ...

But after words like hvernig, Icelandic normally does not use main-clause V2 in the same way. The subject often comes before the verb in a more straightforward order:

• hvernig sögnin lítur út

So here:

• sögnin = subject
• lítur út = verb phrase

That is normal subordinate-clause word order.

Lítur út is the verb líta út, which means to look or to appear.

So:

• líta út = look / appear
• lítur út = looks / appears

This is a common kind of Icelandic verb where the meaning belongs to the whole expression, not just the first word by itself.

Examples:

• Hann lítur út fyrir að vera þreyttur. = He looks like he is tired.
• Sögnin lítur út svona. = The verb looks like this.

In your sentence, lítur út means something like looks / appears in form.

Because sögnin is the subject of the verb lítur út.

Inside the embedded clause:

• sögnin = the thing doing the looking/appearing
• lítur út = the verb

Subjects are normally in the nominative in Icelandic, so sögnin is nominative here.

Yes, á morgun is a very common expression meaning tomorrow.

It is best learned as a set phrase.

Literally, á often means on, and historically this expression involves a case form of morgunn (morning), but for learners the most useful thing is simply:

• á morgun = tomorrow

Other useful time expressions built in a similar way include:

• í dag = today
• í gær = yesterday

Because framtíð here is being used as a more general or abstract noun: future.

Icelandic often leaves out the article with abstract ideas where English may or may not use one depending on context.

So:

• í framtíð = in the future

In grammar explanations, the exact interpretation depends on context. It can refer generally to the future, or in some contexts to future form/time reference. The important point for structure is that í framtíð is a prepositional phrase headed by í.

Because each verb agrees with a singular subject:

• sýnir matches kennarinn = the teacher
• lítur matches sögnin = the verb

Both kennarinn and sögnin are singular nouns, so the verbs are in 3rd person singular.

Only partly. Some parts line up neatly, but not everything should be understood too literally.

Roughly:

• Á morgun = tomorrow
• sýnir = shows
• kennarinn = the teacher
• hvernig = how
• sögnin = the verb
• lítur út = looks / appears
• í framtíð = in the future

But the natural English translation may need slight adjustment depending on context, especially because:

• Icelandic uses the present for future meaning here
• líta út is an expression, not just a literal look out
• í framtíð may be interpreted a little differently depending on what exactly is being taught

So it is better to understand the sentence by structure and usage, not only by matching one word to one word.