Jeg vrider håndklædet, før jeg hænger det på tørresnoren.

Because håndklædet is the definite form of the noun: the towel.

• et håndklæde = a towel
• håndklædet = the towel

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

Since the sentence refers to a specific towel, Danish uses håndklædet.

Det refers back to håndklædet.

In English, we would say:

• I wring the towel before I hang it on the clothesline.

Here, it = the towel.
In Danish:

• håndklædet = the towel
• det = it

This works because håndklæde is a neuter noun (et-word), so the pronoun is det.

Because vrider is the present tense form of the verb at vride.

• at vride = to wring / twist
• jeg vrider = I wring / I am wringing

In Danish, the present tense usually ends in -r:

• at hænge → hænger
• at vride → vrider

So jeg vrider is the normal present-tense form.

Før means before.

It connects the two parts of the sentence:

• Jeg vrider håndklædet = I wring the towel
• før jeg hænger det på tørresnoren = before I hang it on the clothesline

So før introduces a time relationship: one action happens before another.

Because after før, Danish uses subordinate clause word order.

In a subordinate clause, the subject usually comes before the verb:

• før jeg hænger det på tørresnoren

not

• før hænger jeg det på tørresnoren

So the order is:

• før
  • subject
    • verb
      • rest

This is different from main clauses, where Danish often has verb-second word order.

Because det is the direct object, and it normally comes before adverbial phrases like på tørresnoren.

So the structure is:

• jeg hænger = I hang
• det = it
• på tørresnoren = on the clothesline

Danish word order here is very natural and matches English fairly closely:

• I hang it on the clothesline
• jeg hænger det på tørresnoren

• hænge is the infinitive: to hang
• hænger is the present tense: hang / am hanging

Examples:

• at hænge tøj op = to hang up clothes
• jeg hænger det op = I hang it up / I’m hanging it up

In your sentence, hænger is used because the subject is jeg and the action is happening in the present.

Because på means on, and a towel is hung on a clothesline, not in it.

• på tørresnoren = on the clothesline

This is similar to English usage. Danish often uses på for something resting on or attached to a surface or line.

Tørresnoren means the clothesline or more literally the drying line.

It is made up of:

• tørre = to dry
• snor = string / cord / line
• snoren = the line
• tørresnoren = the drying line / clothesline

So it is a compound noun, which is very common in Danish.

Because Danish punctuation normally uses a comma before a subordinate clause.

Since før jeg hænger det på tørresnoren is a subordinate clause, the comma is standard:

• Jeg vrider håndklædet, før jeg hænger det på tørresnoren.

English punctuation is sometimes less strict here, but in Danish this comma is very common and often expected.

Yes, vrider is a very natural verb here.

At vride suggests twisting something to squeeze water out of it, which fits a towel very well.

So this sentence gives the image of physically twisting the towel before hanging it up to dry.

Then you would say:

• Jeg vrider et håndklæde, før jeg hænger det på tørresnoren.

Here:

• et håndklæde = a towel
• det = it

Even though the first mention is indefinite, you can still use det afterward to refer back to that towel.

However, in many real situations, håndklædet sounds more natural because the speaker usually means a specific towel.

It looks long because it contains several parts:

• hånd = hand
• klæde = cloth
• -t = definite ending

So literally it is something like the hand-cloth, which is Danish for the towel.

A learner should also know that Danish pronunciation is often less transparent than the spelling suggests. In normal speech, parts of the word may sound softer or less clearly pronounced than expected from the written form. So it is worth listening to native audio for this word rather than relying only on spelling.

Yes. Inden can also mean before in this kind of sentence.

So this would also be correct:

• Jeg vrider håndklædet, inden jeg hænger det på tørresnoren.

In many contexts, før and inden are both possible.
For learners, før is often the simpler and more common choice to recognize early on.