Jeg vrider vaskekluden, før jeg tørrer bordet af.

Because Danish, like German, very often forms compound nouns as a single word.

• vaskeklud = washcloth
• vaske relates to washing
• klud = cloth

Then -en is added to make it definite:

• en vaskeklud = a washcloth
• vaskekluden = the washcloth

So vaskekluden literally breaks down as washcloth-the.

Vrider is the present tense of at vride.

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

In this sentence, it means to wring out the washcloth, as you would do after getting it wet.

Because Danish normally needs a full clause after før.

So you have:

• Jeg vrider vaskekluden = first clause
• før jeg tørrer bordet af = second clause

Just like in English, you usually repeat the subject:

• I wring the washcloth before I wipe the table off

You would not normally leave out jeg here.

Because før introduces a subordinate clause, and subordinate clauses in Danish normally keep subject + verb order.

So:

• før jeg tørrer bordet af = correct

If you said før tørrer jeg..., that would sound wrong here because it uses main-clause word order.

A useful contrast:

• Main clause: Nu tørrer jeg bordet af.
• Subordinate clause: før jeg tørrer bordet af

Because at tørre af is a verb + particle combination, similar to English to wipe off or to wipe down.

In Danish, with a full noun as the object, the particle often comes after the object:

• jeg tørrer bordet af

Compare English:

• I wipe the table off
• I wipe off the table

Danish strongly prefers tørre bordet af in this kind of sentence.

So af belongs with the verb, but it appears later in the clause.

Tørre bordet af usually means to wipe the table off / wipe down the table, especially when cleaning it.

By contrast, tørre bordet can sound more like dry the table or make the table dry.

So:

• tørre bordet af = wipe the surface clean
• tørre bordet = dry the table

In this sentence, af makes the cleaning meaning clearer and more natural.

Because før jeg tørrer bordet af is a subordinate clause, and many Danish writers put a comma before such clauses.

However, this is a point where Danish punctuation has some variation depending on comma style. You may also see:

• Jeg vrider vaskekluden før jeg tørrer bordet af.

So the comma is normal, but its presence can depend on which official comma system the writer follows.

It is in the present tense:

• vrider
• tørrer

But present tense in Danish, like in English, is not only for something happening right now. It can also describe:

• a routine
• a general habit
• a step in a process
• an instruction-like sequence

So the sentence can mean something like This is what I do: first I wring the washcloth, then I wipe the table.

Yes, often you can.

• før jeg tørrer bordet af
• inden jeg tørrer bordet af

Both can mean before I wipe the table off.

A rough difference is:

• før is the basic, very common word for before
• inden can sometimes sound a bit more focused on before that point in time

In many everyday sentences like this one, either works.

Yes. Bordet is the definite singular form of bord.

• et bord = a table
• bordet = the table

So Danish adds the definite ending directly to the noun:

• -en for many common-gender nouns, as in vaskekluden
• -et for many neuter nouns, as in bordet

That is why there is no separate word for the in front of these nouns.