Ræktunin byrjar núna.

Because -in is the definite article attached to the noun. Icelandic often says the by adding it to the end of the word instead of using a separate word like English does.

• ræktun = cultivation / growing
• ræktunin = the cultivation / the growing

So ræktunin is not a different basic word; it is the noun ræktun with the built into it.

In Icelandic, the definite article is usually a suffix, not a separate word.

So instead of:

• English: the cultivation

you often get:

• Icelandic: ræktunin

There is also a separate article in Icelandic in some contexts, but for ordinary definite nouns, the attached article is the normal choice.

Byrjar is the present tense, 3rd person singular form of the verb byrja (to begin, to start).

Here is the basic idea:

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

In Ræktunin byrjar núna, the subject is ræktunin, which is singular, so the verb is also singular: byrjar.

Because byrja is the infinitive form, meaning to begin.

In a normal sentence, Icelandic usually uses a conjugated verb, not the infinitive. Since the subject is ræktunin (the cultivation), the correct finite verb form is byrjar:

• að byrja = to begin
• ræktunin byrjar = the cultivation begins

So byrja would only be used in places where English would use to begin, such as after another verb.

It is in the nominative case because it is the subject of the sentence.

In this sentence, ræktunin is the thing doing the action of beginning:

• Ræktunin = subject
• byrjar = verb
• núna = adverb

So the nominative is exactly what you would expect here.

Ræktun is feminine.

That matters because Icelandic noun gender affects things like:

• the form of the definite article
• adjective endings
• pronouns that refer back to the noun

In this sentence, you do not need a separate adjective or pronoun, but knowing that ræktun is feminine is still useful for building other sentences correctly.

Núna means now. It is an adverb of time.

So the sentence structure is:

• Ræktunin = the cultivation
• byrjar = begins
• núna = now

Together: The cultivation begins now.

It tells you when the action happens.

Both can mean now.

Very roughly:

• nú can feel a little shorter or more direct
• núna is very common in everyday speech and often feels natural in ordinary conversation

In many contexts they are close in meaning, but núna is a very normal choice in a sentence like this.

This is a very normal Icelandic main-clause word order:

• subject
  • verb
    • adverb

So:

• Ræktunin = subject
• byrjar = verb
• núna = time adverb

That gives a neutral statement.

You could also move núna for emphasis, for example:

• Núna byrjar ræktunin.

That would put more focus on now. But the original sentence is the most straightforward, neutral version.

Without the definite article, it would be:

• Ræktun byrjar núna.

Grammatically, that means something more like cultivation begins now or cultivation is beginning now, which is less natural in many contexts unless you mean the idea in a general or abstract sense.

The version with the article:

• Ræktunin byrjar núna

usually points to a specific cultivation/growing process already understood from context: the cultivation.

A rough learner-friendly guide:

• ræ in ræktunin sounds roughly like rye
• kt is pronounced clearly
• u in Icelandic is not like English oo; it is more fronted
• byrjar begins with b
  • a vowel somewhat like the Icelandic y, which does not have an exact English match
• núna starts with noo-like nú, though the Icelandic vowel is longer and cleaner than in many English accents

A very rough approximation might be:

• RYEK-tu-nin BIR-yar NOO-na

But that is only approximate. The vowels in Icelandic are important, so it is best to listen to native audio if possible.

Yes. In many contexts, byrja can be translated as either begin or start.

So Ræktunin byrjar núna could be rendered as:

• The cultivation begins now
• The cultivation starts now

English chooses between begin and start mostly based on style and context, not because Icelandic is making a strong distinction here.