I det lille rum står der nu en reol ved siden af skrivebordet.

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

Here, I det lille rum is placed first for emphasis or as the topic:

• I det lille rum = first position
• står = second position

So Danish says:

• I det lille rum står der nu en reol ...

If you started with der, you could also say:

• Der står nu en reol i det lille rum ...

Both are grammatical, but the first version puts more focus on the room.

Here, der is an expletive or dummy subject, much like English there in there is or there stands.

So in this sentence, der does not mainly mean a physical location like there over there. Instead, it helps form an existential sentence: a sentence that says something exists or is present somewhere.

Compare:

• English: There is now a bookcase ...
• Danish: Der står nu en reol ...

So der is part of the structure, not the main meaning.

Danish often uses position verbs where English would simply use is.

Common ones are:

• stå = stand
• ligge = lie
• sidde = sit

A reol (bookcase / shelving unit) is thought of as an upright object, so it stands:

• Der står en reol = There is a bookcase / A bookcase is standing

In natural English, we usually just say there is a bookcase, but Danish prefers the more physical verb here.

In Danish, when a noun is definite and has an adjective, the usual pattern is:

• den/det/de + adjective + noun in the indefinite form

So:

• det lille rum = the small room

Not:

• det lille rummet ❌

Without an adjective, you would use the definite ending on the noun:

• rummet = the room

So the contrast is:

• rummet = the room
• det lille rum = the small room

Because rum is a neuter noun in Danish.

Danish has two grammatical genders:

• common gender: usually takes en
• neuter: usually takes et

Since rum is neuter:

• et rum = a room
• det lille rum = the small room

By contrast, reol is common gender:

• en reol = a bookcase

So the articles agree with the noun’s gender.

Because en reol is indefinite, while skrivebordet is definite.

• en reol = a bookcase
• skrivebordet = the desk

In this sentence, the bookcase is being introduced as something new, so Danish uses the indefinite form:

• en reol

The desk is treated as a specific, identifiable desk, so Danish uses the definite form:

• skrivebordet

This is very similar to English a vs the.

Nu means now.

It suggests that this is the current situation, often with an implied contrast to before:

• There is now a bookcase ...
• maybe before, there was no bookcase

Its position here is natural in Danish existential word order:

• står der nu en reol

You may see nu in other positions too, but this placement is very normal and neutral.

Ved siden af is a fixed expression meaning:

• next to
• beside

So:

• ved siden af skrivebordet = next to the desk

The af is simply part of this expression. You should learn ved siden af as a whole chunk.

Examples:

• ved siden af huset = next to the house
• ved siden af mig = next to me

Because skrivebord is a neuter noun, and the normal definite singular ending for many neuter nouns is -et.

So:

• et skrivebord = a desk
• skrivebordet = the desk

This matches rum:

• et rum
• rummet

By contrast, many common-gender nouns take -en in the definite singular:

• en reol
• reolen

Yes. That is also grammatical.

The difference is mainly focus:

• I det lille rum står der nu en reol ...
  Focuses first on the room
• Der står nu en reol i det lille rum ...
  Presents the existence of the bookcase more neutrally first

Danish allows this kind of reordering because of the V2 rule, but the emphasis changes depending on what comes first.

Not always.

Reol usually means something more like:

• bookcase
• shelving unit
• set of shelves

A single shelf is more often:

• en hylde

So in many contexts, en reol is better understood as a bookcase or a shelving unit rather than just a shelf.