Jeg skifter dynebetrækket, når det gamle begynder at lugte af støv.

Because Danish, like German, makes a lot of compound nouns by joining words together.

Here:

• dyne = duvet
• betræk = cover

So dynebetræk means duvet cover, and the definite form is dynebetrækket = the duvet cover.

The last part of the compound is the main noun, so betræk determines the gender and the definite ending.

The ending -et is the singular definite ending for a neuter noun.

• et betræk = a cover
• betrækket = the cover

Since dynebetræk is built on betræk, it stays neuter:

• et dynebetræk = a duvet cover
• dynebetrækket = the duvet cover

So -et here is not random; it shows the.

Danish often uses det/den + adjective to mean the ... one when the noun is understood from context.

So det gamle means the old one, referring back to dynebetrækket.

English does this too:

• I replace the duvet cover when the old one starts to smell dusty.

Danish avoids repeating the noun because it is already clear what is being talked about.

Because dynebetræk is a neuter noun, an et-word.

In Danish:

• den is used with common-gender nouns
• det is used with neuter nouns

Since the hidden noun is dynebetræk, the correct form is:

• det gamle = the old one

If the noun were a den-word, you would use den gamle instead.

Here skifter means change or replace in the sense of swapping one thing for another.

So Jeg skifter dynebetrækket means:

• I change the duvet cover
• or I replace the duvet cover

It does not mean change in the sense of becoming different. It means taking off one cover and putting on another.

Because Danish often uses the present tense for habitual actions and general situations.

This sentence describes something that happens regularly:

• I change the duvet cover when the old one starts to smell of dust.

It is not talking about one single event happening right now. It is more like a routine or rule.

This is very similar to English:

• I change it when... not necessarily
• I am changing it when...

Here når means when or whenever.

It is used because the speaker expects this situation to happen as part of normal life:

• when the old one starts to smell of dust

By contrast, hvis means if and is more conditional or uncertain.

Compare:

• Jeg skifter dynebetrækket, når det gamle begynder at lugte af støv.
  = I change the duvet cover when/whenever the old one starts to smell of dust.
• Jeg skifter dynebetrækket, hvis det gamle begynder at lugte af støv.
  = I’ll change the duvet cover if the old one starts to smell of dust.

Both are possible in some contexts, but når sounds more like a regular expected occurrence.

Because begynde is normally followed by an infinitive with at.

So:

• begynde at lugte = begin to smell

This is a very common pattern in Danish:

• begynde at læse = begin to read
• begynde at arbejde = begin to work

So the at here works like English to in begin to smell.

Because lugte af is the normal expression for smell of or smell like.

So:

• lugte af støv = smell of dust
• lugte af røg = smell of smoke
• lugte af kaffe = smell of coffee

This is just the standard preposition used with this meaning.

A useful distinction is:

• lugte af noget = smell of something
• lugte noget = smell something, in the sense of detecting it with your nose

So in this sentence, lugte af støv means the duvet cover has a dusty smell.

Because støv is being used as an uncountable mass noun, just like dust in English.

So Danish says:

• lugte af støv = smell of dust

Not:

• lugte af et støv

You generally do not use an article with substances or materials when talking about them in a general way.

Because Danish normally puts a comma before a subordinate clause.

The part starting with når is a subordinate clause:

• når det gamle begynder at lugte af støv

So the comma is standard Danish punctuation.

This is something learners often notice because Danish uses commas more consistently before subordinate clauses than English does.

Yes. You could also say:

Når det gamle begynder at lugte af støv, skifter jeg dynebetrækket.

That is perfectly natural.

But notice the word order in the main clause:

• skifter jeg not
• jeg skifter

That happens because Danish is a verb-second language in main clauses. When another element comes first, the finite verb still takes second position.

So:

• Jeg skifter dynebetrækket, når...
• Når ..., skifter jeg dynebetrækket.

Both are correct; the difference is mainly what you choose to emphasize first.