Hundanámskeiðið byrjar á morgun.

It is a compound word:

• hunda- = dog / dogs in a compound form
• námskeið = course, class, or training course
• -ið = the (the definite article attached to the noun)

So hundanámskeiðið means the dog-training course or the dog class.

Icelandic often packs a lot into one long compound word, where English would use several separate words.

In Icelandic, the definite article is usually suffixed to the noun instead of being a separate word.

So:

• námskeið = course
• námskeiðið = the course

And with a compound:

• hundanámskeið = dog-training course
• hundanámskeiðið = the dog-training course

So the article goes on the whole noun, at the very end.

Because Icelandic compounds often use a stem or genitive-based form rather than the plain dictionary form.

The dictionary form is:

• hundur = dog

But in this compound, it becomes:

• hunda-

This gives the sense of dog-related or of dogs, so hundanámskeið is literally something like a course of/for dogs.

This is very common in Icelandic compounds, so learners often need to get used to the fact that the first part of a compound may not look exactly like the basic dictionary form.

Byrjar is the present tense, 3rd person singular of the verb byrja = to begin / to start.

So:

• ég byrja = I begin
• þú byrjar = you begin
• hann/hún/það byrjar = he/she/it begins

Here the subject is hundanámskeiðið, which is singular, so the verb is singular too:

• Hundanámskeiðið byrjar = The dog-training course begins

Because Icelandic, like English, often uses the present tense for scheduled future events.

Compare English:

• The course starts tomorrow.

That is present tense in form, but future in meaning.

Icelandic does the same:

• Hundanámskeiðið byrjar á morgun.

So there is no need for a separate word meaning will here.

Á morgun is the normal Icelandic expression for tomorrow.

Word-for-word, it may look a bit like on tomorrow, but you should learn it as a fixed time expression:

• á morgun = tomorrow

A very useful contrast is:

• í morgun = this morning
• á morgun = tomorrow

So even though morgun is related to morning, the full expression á morgun specifically means tomorrow.

Here it is in the nominative singular, because it is the subject of the sentence.

• Hundanámskeiðið = the thing that is starting
• byrjar = starts

So the sentence structure is basically:

• [Subject] + [Verb] + [Time expression]

Also, námskeið is a neuter noun, which is why the definite ending is -ið.

Yes. Icelandic word order is somewhat flexible, but it follows an important verb-second pattern.

The neutral order here is:

• Hundanámskeiðið byrjar á morgun.

You can also move the time expression to the front:

• Á morgun byrjar hundanámskeiðið.

That still means The dog-training course starts tomorrow.

But if you front á morgun, the verb byrjar normally stays in second position. That is a very important Icelandic pattern.

A rough English-friendly approximation is:

• HUN-da-nowm-skay-thith BIR-yar ow MOR-gun

A few helpful points:

• á is pronounced roughly like ow in now
• ei in skeið is roughly like ay in say
• ð is like the th in this
• j is pronounced like English y

So byrjar sounds roughly like BIR-yar, not like an English j sound.

It can mean more than just an academic course. Námskeið is often used for:

• a course
• a class
• a training course
• a workshop-like course

So in this sentence, hundanámskeiðið could naturally mean something like:

• the dog-training course
• the dog class
• the dog training class

The exact English translation depends on context.