Jeg tørrer bordet af med en ren klud, før gæsterne kommer.

Because tørre af is a very common verb + particle combination in Danish meaning to wipe off / wipe down.

So:

• tørre on its own can mean to dry or sometimes to wipe
• tørre af specifically gives the idea of wiping a surface clean

In this sentence, Jeg tørrer bordet af means I wipe the table down / off.

In Danish, particles like af, op, ud, and på often come after the object in ordinary main clauses.

So Danish says:

• Jeg tørrer bordet af

not usually:

• Jeg tørrer af bordet

That word order is very natural in Danish and is something English speakers just have to get used to.

Bordet is the definite form of bord:

• et bord = a table
• bordet = the table

Danish usually adds definiteness to the end of the noun instead of using a separate word like the.

So:

• bord = table
• et bord = a table
• bordet = the table

Gæsterne is the definite plural form of gæst.

• en gæst = a guest
• gæster = guests
• gæsterne = the guests

Again, Danish often marks definiteness by adding an ending to the noun:

• singular definite: often -en or -et
• plural definite: often -ne

So gæsterne kommer = the guests are coming.

Because klud is a common-gender noun, so it takes en, not et.

• en klud = a cloth

And the adjective has to match the noun form:

• en ren klud = a clean cloth

Compare:

• et rent bord = a clean table

So the adjective changes depending on gender and form:

• common gender singular indefinite: ren
• neuter singular indefinite: rent
• plural / definite: often rene

Danish often uses the present tense to talk about the future when the time is clear from context.

So:

• før gæsterne kommer literally uses present tense
• but it means before the guests come / before the guests arrive

English does something similar in time clauses:

• before the guests come
• not usually before the guests will come

So this is very normal Danish.

Med means with, and here it introduces the tool or instrument used to do the action.

So:

• med en ren klud = with a clean cloth

It tells you how the table is being wiped.

It is a subordinate clause introduced by før.

The main clause is:

• Jeg tørrer bordet af med en ren klud

The subordinate clause is:

• før gæsterne kommer

That subordinate clause tells us when the action in the main clause happens.

So the whole sentence means something like:

• I wipe the table down with a clean cloth before the guests come

The comma is there because før gæsterne kommer is a subordinate clause, and many Danish writers put a comma before such clauses.

However, this is a bit tricky, because modern Danish accepts two comma systems:

• a system that uses a comma before subordinate clauses
• a system that often leaves it out

So both of these may be accepted depending on the system being followed:

• Jeg tørrer bordet af med en ren klud, før gæsterne kommer.
• Jeg tørrer bordet af med en ren klud før gæsterne kommer.

The version with the comma is very common.

Yes, før is very natural here.

It is commonly used before a clause:

• før gæsterne kommer = before the guests come

Learners sometimes also meet inden or inden at, but før is the most straightforward choice in this sentence.

Not always. Tørre can also relate to drying.

For example:

• at tørre can mean to dry
• at tørre noget af can mean to wipe something off / wipe something down

So context matters. In this sentence, because of bordet af, the meaning is clearly to wipe the table down.