Hvis håndklædet er beskidt, tager jeg et nyt.

Because håndklædet is the definite form: the towel.

• et håndklæde = a towel
• håndklædet = the towel

In Danish, the definite article is often added to the end of the noun instead of being a separate word like English the.

Since the sentence means If the towel is dirty..., Danish uses håndklædet.

Because håndklæde is a neuter noun, and the adjective agrees with it.

• en-words often use the basic adjective form
• et-words often add -t in singular

So:

• en beskidt skjorte = a dirty shirt
• et beskidt håndklæde = a dirty towel

The same agreement also appears when the adjective comes after er:

• Håndklædet er beskidt = The towel is dirty

You mainly have to learn the gender along with the noun.

The dictionary form is:

• et håndklæde

That tells you it is a neuter noun. This affects several things:

• the indefinite article: et håndklæde
• the definite form: håndklædet
• adjective agreement: et nyt håndklæde, håndklædet er beskidt

Unfortunately, Danish noun gender is not always predictable, so it is best to memorize the article together with the noun.

Because Danish uses verb-second word order in main clauses.

The first part, Hvis håndklædet er beskidt, is a subordinate clause. When that whole clause comes first, the finite verb in the main clause must come before the subject:

• Hvis håndklædet er beskidt, tager jeg et nyt.

Literally, the structure is:

• If the towel is dirty, take I a new one

But in natural English we say:

• If the towel is dirty, I take a new one

This verb-second pattern is very important in Danish:

• Jeg tager et nyt.
• I dag tager jeg et nyt.
• Hvis håndklædet er beskidt, tager jeg et nyt.

In all of these, the finite verb is in the second position of the main clause.

Hvis means if.

It introduces a condition:

• Hvis håndklædet er beskidt... = If the towel is dirty...

This is the normal word to use for if in Danish conditional sentences.

Because the sentence begins with a subordinate clause:

• Hvis håndklædet er beskidt

  and then continues with the main clause:

• tager jeg et nyt

The comma marks the boundary between those two clauses. In a sentence like this, that comma is standard and very helpful for reading the structure clearly.

Because the hidden noun is håndklæde, which is an et-word.

Et nyt really means:

• et nyt håndklæde = a new towel

But Danish often leaves out the noun when it is obvious from context, just like English says a new one.

So:

• Jeg tager et nyt = I take a new one
• understood as: I take a new towel

Also note that ny is irregular:

• en ny ...
• et nyt ...
• nye ...

Because et nyt functions as a complete noun phrase meaning a new one.

Even though håndklæde is omitted, Danish still keeps the article and adjective:

• et nyt = a new one

This is very similar to English:

• I need a towel. I’ll take a new one.

Danish does not need a separate word for one here; et nyt is enough.

Literally, tager comes from at tage, meaning to take.

In this sentence, though, the natural English meaning is more like:

• I take a new one
• I get a new one
• I use a fresh one

So Danish uses tage in places where English might choose different verbs depending on context.

Yes.

The adjective is:

• ny = new

Its forms are:

• ny for common gender singular
• nyt for neuter singular
• nye for plural and definite contexts

Examples:

• en ny bog = a new book
• et nyt håndklæde = a new towel
• nye bøger = new books

So in et nyt, the -t matches the neuter noun håndklæde.

No, that is not standard Danish word order.

After the initial hvis-clause, the main clause must keep verb-second order:

• Hvis håndklædet er beskidt, tager jeg et nyt. ✅

Not:

• Hvis håndklædet er beskidt, jeg tager et nyt. ❌

This is one of the biggest differences from English, since English would normally keep I take after an introductory clause.

It is in the present tense:

• er = is
• tager = take

Depending on context, it can mean either:

• a present/future situation: If the towel is dirty, I’ll take a new one
• a habitual action: If the towel is dirty, I take a new one

Danish present tense often covers both meanings, and the exact interpretation comes from context.

In this sentence, yes, that is the natural interpretation.

Because the previous noun is håndklædet, et nyt clearly means:

• a new towel
• literally: a new one

This kind of omission is very common in Danish when the noun is already understood from the context.