Hun tager sin regnjakke på, så snart det begynder at regne.

Because sin is the reflexive possessive form in Danish.

When the owner is the same person as the subject of the clause, Danish normally uses sin / sit / sine:

• Hun tager sin regnjakke på = she puts on her own raincoat.

If you said hendes, it would usually mean the raincoat belongs to some other female person:

• Hun tager hendes regnjakke på = she puts on her raincoat, meaning someone else’s.

So sin shows that the raincoat belongs to hun.

Here tage ... på means to put on clothing.

So:

• tage en jakke på = to put on a jacket
• tage sko på = to put on shoes

This is a very common Danish verb-particle combination. In this sentence, it refers specifically to putting on the raincoat.

Because tage på works like a separable verb-particle expression.

In Danish, the object often comes between the verb and the particle:

• Hun tager sin regnjakke på
• Han tager skoene af

This is similar to English expressions like:

• put the coat on
• take the shoes off

So tager and på belong together in meaning, even though another element appears between them.

Because Danish uses det as a dummy subject with weather expressions.

Just as English says:

• it is raining

Danish says:

• det regner

So if you say it begins to rain, Danish naturally becomes:

• det begynder at regne

The det does not refer to a specific thing. It is just the grammatical subject required by the sentence.

Because after begynde, Danish normally uses an infinitive with at.

So:

• begynder at regne = begins to rain
• begynder at synge = begins to sing
• begynder at løbe = begins to run

The at here is like English to in to rain.

Så snart is a conjunction meaning as soon as.

It introduces a subordinate clause:

• så snart det begynder at regne

So the sentence structure is:

• main clause: Hun tager sin regnjakke på
• subordinate clause: så snart det begynder at regne

It is a fixed expression, and it is written as two words: så snart.

Because Danish uses different word-order patterns in main clauses and subordinate clauses.

In the main clause, Danish follows the V2 rule, where the finite verb comes early in the clause:

• Hun tager sin regnjakke på

In the subordinate clause introduced by så snart, Danish does not use that same main-clause pattern:

• så snart det begynder at regne

So this sentence is a good example of the difference between:

• main clause word order
• subordinate clause word order

Because Danish often uses the present tense for habitual actions and for future situations that are tied to a condition or time expression.

Here the meaning is something like:

• whenever it starts raining, she puts on her raincoat
• as soon as it starts raining, she will put on her raincoat

This is very similar to English, which also often uses the present after words like when or as soon as:

• As soon as it starts raining, she puts on her raincoat

So the present tense is completely natural here.

Because Danish usually writes compound nouns as a single word.

So:

• regn
  • jakke = regnjakke

This is very common in Danish:

• sommerferie
• togstation
• regnvejr

English often writes these as two words or with different spelling habits, but Danish strongly prefers one-word compounds.

Yes, you could, but the meaning changes slightly.

• så snart det begynder at regne focuses on the moment the rain starts
• så snart det regner focuses more generally on the state of it raining

So the original sentence is a bit more precise if you want the idea the moment it starts raining.

Because the sentence as written uses a comma before the subordinate clause.

However, this is one of those areas where Danish punctuation can vary depending on comma style. You may also see:

• Hun tager sin regnjakke på så snart det begynder at regne.

So if you notice both versions, that is normal. The version with the comma is common and fully natural.

No. Regne can also mean to calculate or to count in other contexts.

For example:

• Det regner = it is raining
• Jeg kan regne = I can calculate

In this sentence, because of det begynder at regne, the meaning is clearly the weather verb to rain.