Jeg vil hellere have den, som ligger på bordet.

Hellere means rather and is used to express preference.

So vil hellere have is the Danish way to say that someone would prefer one thing over another.

A useful mini-pattern is:

• gerne = gladly / with pleasure
• hellere = rather
• helst = preferably / most of all

So here, hellere shows comparison: this option is preferred to some other option.

Because Danish main clauses normally follow the verb-second rule: the finite verb comes early in the sentence, usually in second position.

Here:

• Jeg = subject
• vil = finite verb
• hellere = adverb
• have = infinitive

So the normal neutral order is:

Jeg vil hellere have ...

That placement of hellere is very common: it usually comes after the finite verb and before the infinitive.

Because vil is a modal verb, and modal verbs in Danish normally take a bare infinitive.

So you say:

• Jeg vil have den
• Jeg kan se det
• Du skal gå nu

not:

• Jeg vil at have den

This is similar to English I will go, not I will to go.

Yes, have literally means have, but in Danish vil have is very common and can mean want to have, want to get, want to receive, or want to choose, depending on context.

So in a sentence like this, have does not sound strange to a Dane. It is a very natural way to talk about wanting a particular item.

Because den and det depend on the grammatical gender of the noun being referred to.

• den = common gender
• det = neuter gender

In this sentence, den stands for some understood noun of common gender, such as bogen, koppen, trøjen, etc.

If the hidden noun were neuter, you would use det instead:

• Jeg vil hellere have det, som ligger på bordet.

So den does not mean the here; it means that one / it, referring back to an understood noun.

Som introduces a relative clause: a clause that describes or identifies something.

Here, som ligger på bordet describes den.

So som works like English that, which, or sometimes who, depending on context.

A key point for learners: Danish som does not change form the way English does. It can be used for both people and things.

Yes, you often can.

A very common alternative is:

Jeg vil hellere have den, der ligger på bordet.

In modern Danish, especially in everyday language, der is very common in relative clauses when it is the subject of the clause, as it is here.

So both of these are natural:

• den, som ligger på bordet
• den, der ligger på bordet

For a learner, it is safest to remember that both can occur here, though der may sound a bit more everyday to many speakers.

Because Danish often uses position verbs where English would simply use be.

Common ones are:

• ligge = lie / be lying
• stå = stand / be standing
• sidde = sit / be sitting

If an object is resting flat on a surface, Danish often says it lies there:

• Bogen ligger på bordet.

So ligger is more natural than er here.

På means on, so på bordet means on the table.

Bordet is the definite form of bord:

• et bord = a table
• bordet = the table

Danish usually makes nouns definite by adding an ending to the noun, instead of putting a separate word like English the in front.

Since bord is a neuter noun, its definite ending is -et.

This is about Danish comma style.

Many Danes write a comma before a subordinate or relative clause, so:

Jeg vil hellere have den, som ligger på bordet.

But in modern Danish, the so-called start comma is optional in many contexts, so you may also see:

Jeg vil hellere have den som ligger på bordet.

So the comma is not mainly about changing the meaning the way it often does in English; it is more about which Danish comma system or style is being used.

Yes, it is natural Danish.

A very common spoken alternative would be:

Jeg vil hellere have den, der ligger på bordet.

That version may sound a little more everyday to some speakers, but the original sentence is perfectly good Danish.

So as a learner, you can treat the original as correct and useful, while also recognizing that der is a common alternative to som in this kind of sentence.