Hvis jeg havde fundet støvsugeren tidligere, ville jeg have gjort stuen ren, før gæsterne kom.

This is a past unreal conditional — the same basic idea as the English third conditional.

Pattern:

• Hvis
  • past perfect = the unreal condition
• ville
  • have
    • past participle = the unreal result

So:

• Hvis jeg havde fundet støvsugeren tidligere = If I had found the vacuum cleaner earlier
• ville jeg have gjort stuen ren = I would have cleaned the living room

It describes something that did not actually happen in the past.

Havde fundet is the past perfect.

It is formed with:

• havde = had
• fundet = found

Danish uses this here for the same reason English uses had found: it refers to something imagined as happening before another past situation.

So Hvis jeg havde fundet ... means If I had found ... — implying that in reality, the speaker did not find it in time.

This is because Danish main clauses follow the V2 rule: the finite verb must come in second position.

Here, the whole Hvis ... clause comes first:

• Hvis jeg havde fundet støvsugeren tidligere

That first clause takes the first slot, so in the main clause the finite verb must come next:

• ville jeg have gjort stuen ren

So the order is:

1. fronted clause
2. finite verb
3. subject

If the main clause came first, you would get:

• Jeg ville have gjort stuen ren, hvis jeg havde fundet støvsugeren tidligere.

Because hvis and før introduce subordinate clauses, and subordinate clauses do not use normal main-clause V2 word order.

After a subordinating word like hvis, før, fordi, at, the normal pattern is:

• conjunction
• subject
• finite verb

So:

• hvis jeg havde fundet
• før gæsterne kom

That is different from the main clause:

• ville jeg have gjort ...

So this sentence is a good example of both systems:

• subordinate clause order after hvis and før
• main clause V2 order in ville jeg have gjort ...

Because after a modal verb such as ville, Danish uses the bare infinitive.

Common modal verbs include:

• ville
• kunne
• skulle
• måtte

So you say:

• ville have gjort
• kunne gøre
• skulle gå

not:

• ville at have gjort
• kunne at gøre

So ville jeg have gjort is exactly what you should expect.

Because Danish usually puts the definite article at the end of the noun.

Examples from the sentence:

• støvsuger = vacuum cleaner

• støvsugeren = the vacuum cleaner

• stue = living room

• stuen = the living room

• gæster = guests
• gæsterne = the guests

The endings here are:

• -en for singular definite common gender
• -ne for plural definite

So an English speaker has to get used to the often being attached to the noun rather than standing separately.

Danish often expresses this idea with gøre noget rent/ren, literally make something clean.

So:

• gøre stuen ren = clean the living room
• literally: make the living room clean

This is very natural Danish.

There are also other possible ways to express similar ideas, depending on nuance:

• gøre rent i stuen = clean in the living room / do the cleaning in the living room
• støvsuge stuen = vacuum the living room

But in your sentence, gjort stuen ren works well as a broad idea of cleaning the room.

Because the adjective agrees with the noun.

Here the noun is stuen, from en stue, which is a common-gender noun. With common-gender singular, the adjective form is:

• ren

So:

• gøre stuen ren

If the noun were neuter, you would usually use rent instead:

• et værelse = a room
• gøre værelset rent = clean the room

So the choice between ren and rent depends on the gender of the noun.

Før gæsterne kom is the normal, natural way to say before the guests arrived.

Danish often uses the simple past after før when the sequence is already clear from context.

So:

• før gæsterne kom = before the guests arrived

You could also say:

• før gæsterne var kommet

but that sounds heavier and puts more emphasis on the arrival being already completed before another past point. In this sentence, kom is the most straightforward and idiomatic choice.

Tidligere means earlier.

In this sentence:

• havde fundet støvsugeren tidligere = had found the vacuum cleaner earlier

Its position is natural because adverbs like this often come after the object or toward the end of the clause.

You may sometimes see adverbs moved for emphasis, but this version sounds neutral and normal.

The first comma, after tidligere, separates the opening Hvis clause from the main clause:

• Hvis jeg havde fundet støvsugeren tidligere, ville jeg ...

That comma is expected.

The second comma, before før gæsterne kom, reflects a comma style that uses start commas before subordinate clauses.

So you may see:

• ... stuen ren, før gæsterne kom.

But in modern Danish without start comma, many people would also write:

• ... stuen ren før gæsterne kom.

So the second comma is partly a matter of comma convention, while the first one is much less likely to be omitted.

Yes. Danish can switch the order of the main clause and the hvis clause.

For example:

• Jeg ville have gjort stuen ren, hvis jeg havde fundet støvsugeren tidligere.

This means the same thing.

The main difference is word order in the main clause:

• when the sentence starts with Hvis ..., you get ville jeg
• when the sentence starts with Jeg ..., you get jeg ville

That is again because of the Danish V2 rule in main clauses.