Efter badet tørrer jeg mig med et rent håndklæde.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

Here, Efter badet is placed first, so the verb must come next:

• Efter badet
  • tørrer
    • jeg
      • mig ...

If you start with the subject instead, you get the more neutral order:

• Jeg tørrer mig med et rent håndklæde efter badet.

Both are correct.

Badet is the definite singular form of bad.

• bad = bath / shower / bathing
• badet = the bath / the shower

In this sentence, Danish uses the definite form because it refers to the specific bath or shower just taken. That is very natural in Danish.

It can mean either, depending on context.

In everyday Danish, bad often refers to bathing/washing yourself, and in many situations English would naturally translate it as shower. If you want to be more specific, Danish can also say:

• brusebad = shower
• karbad = bath

So this sentence could naturally be understood as After my shower, I dry myself with a clean towel.

Tørrer is the present tense of at tørre.

It can mean:

• to dry
• to wipe
• to dry off

In jeg tørrer mig, it means I dry myself or I dry off.

Because jeg is the subject form and mig is the object form.

• jeg = I
• mig = me

In this sentence, jeg is the subject doing the action, and mig is the object receiving the action:

• jeg tørrer mig = I dry myself

English uses myself, but Danish uses mig here.

Yes, it is being used reflexively.

Danish works a little differently from English:

• jeg tørrer mig = I dry myself
• du tørrer dig = you dry yourself
• vi tørrer os = we dry ourselves

For first and second person, Danish uses the ordinary object pronouns reflexively:

• mig, dig, os, jer

A special reflexive pronoun, sig, is used mainly for the third person:

• Han tørrer sig = He dries himself

Med means with.

Here it introduces the instrument used to do the action:

• med et rent håndklæde = with a clean towel

So it tells you what you are using to dry yourself.

Because håndklæde is a neuter noun, so it takes:

• the article et
• the adjective ending -t

That gives:

• et rent håndklæde

Compare:

• en ren skjorte = a clean shirt
• et rent håndklæde = a clean towel

So the adjective ren changes to rent to match the neuter noun.

You usually have to learn the gender together with the noun:

• et håndklæde = a towel

Like many Danish nouns, gender is something you mostly memorize as part of the word. Once you know it is et håndklæde, the rest follows naturally:

• et rent håndklæde
• håndklædet = the towel

Because Danish usually writes compound nouns as one word.

So:

• hånd = hand
• klæde = cloth

together become:

• håndklæde = towel

This is very common in Danish. English often writes similar expressions as two words, but Danish normally combines them.

Because Danish often adds the definite article as an ending on the noun.

So:

• bad = bath / shower
• badet = the bath / the shower

That -et ending is doing the job that the does in English.

The same pattern appears with other neuter nouns:

• et håndklæde = a towel
• håndklædet = the towel

Yes, you could.

There is a slight difference in feel:

• Efter badet = after the bath/shower, referring to the specific one in the situation
• Efter et bad = after a bath/shower, a bit more general

Both are grammatical, but Efter badet sounds very natural when talking about your normal routine right after washing yourself.

Yes, absolutely.

That version is also natural and grammatical. The difference is mainly in focus:

• Efter badet tørrer jeg mig ... puts emphasis on after the bath/shower
• Jeg tørrer mig ... efter badet is more neutral and starts with the subject

So the original sentence is not unusual; it just foregrounds the time expression.

In this sentence, yes, rent means clean.

The adjective ren/rent can sometimes mean things like pure in other contexts, but with håndklæde the natural meaning is simply:

• et rent håndklæde = a clean towel