Jeg ville gerne have sådan en lille fjernbetjening til lampen i stuen, hvis den ikke var så dyr.

Vil means want / want to, while ville is the past form, but here it is not really past time. In sentences like this, ville is used much like English would.

So jeg ville gerne have ... hvis ... expresses a hypothetical wish:

• jeg vil gerne have = I want / would like
• jeg ville gerne have = I would like, under certain conditions

Because the sentence also has hvis den ikke var så dyr, the whole thing is unreal or hypothetical: the speaker wants it, but the price is a problem.

Gerne is a very common Danish word that often means something like gladly or with pleasure, but with vil and ville it helps form the idea of would like.

So:

• jeg vil have = I want
• jeg vil gerne have = I would like / I want
• jeg ville gerne have = I would like

It makes the sentence sound more natural and less blunt than just jeg vil have.

Because ville works like a modal verb here, and after modal verbs Danish normally uses the bare infinitive, without at.

So:

• jeg vil have
• jeg kan komme
• jeg skal gå
• jeg ville gerne have

This is similar to English:

• I will go
• I can come
• I would have

You do not say jeg ville gerne at have.

Because Danish normally writes compound nouns as a single word.

So fjernbetjening is one compound:

• fjern = remote
• betjening = operation / control

Together: fjernbetjening = remote control

This is very common in Danish. English often writes these as two words, but Danish usually joins them:

• lampeknap
• fjernbetjening
• stuedør

Sådan en means something like:

• such a
• one like that
• that kind of

It is a very common spoken and everyday way to refer to a thing of that type.

Here, sådan en lille fjernbetjening means something like a little remote control like that.

The form changes with gender and number:

• sådan en for common gender: sådan en lampe
• sådan et for neuter: sådan et bord
• sådan nogle for plural: sådan nogle lamper

Lille is a special adjective in Danish. In modern Danish, lille is the normal form used for singular nouns in this kind of phrase.

So:

• en lille fjernbetjening
• et lille hus

The plural is usually små:

• små fjernbetjeninger

There is also a form liden, but it is rare and mostly literary or old-fashioned. For everyday Danish, lille is the form learners should focus on.

Here til means for use with / intended for / connected to. The remote control is meant to be used with the lamp.

So:

• en fjernbetjening til lampen = a remote control for the lamp

Using for would sound less natural here. In Danish, til is often used when something belongs with or is intended for another object:

• en nøgle til døren
• en oplader til telefonen
• en fjernbetjening til lampen

Because the speaker is talking about specific, known things:

• lampen = the lamp
• stuen = the living room

So this is not just any lamp or any living room. It is a particular lamp in a particular room, probably one both speaker and listener can identify.

This is very normal in Danish, especially when talking about parts of a home:

• i køkkenet
• i stuen
• på badeværelset

It most naturally describes lampen.

So the structure is:

• en lille fjernbetjening
• til lampen
• i stuen

In other words: a little remote control for the lamp in the living room

The idea is not usually that the remote control itself is in the living room, but that the lamp is the one located there.

Most naturally, den refers to fjernbetjeningen, the remote control.

That makes the most sense because the speaker wants the remote control, but says they would want it if it were not so expensive.

Grammatically, both fjernbetjening and lampe are common-gender nouns, so den could in theory refer to either one. But from the meaning of the sentence, the remote control is clearly the intended referent.

Because after a subordinating conjunction like hvis, Danish uses subordinate clause word order.

In a subordinate clause, the sentence adverbial such as ikke usually comes before the finite verb:

• hvis den ikke var så dyr

Compare that with a main clause:

• den var ikke så dyr

So:

• main clause: subject + verb + ikke
• subordinate clause: subject + ikke
  • verb

This is one of the most important word-order differences in Danish.

Because Danish often uses the past tense in hypothetical or unreal conditions, just like English does.

Compare:

• hvis den ikke er så dyr = if it is not that expensive
• hvis den ikke var så dyr = if it were not so expensive

In your sentence, ville and var work together to show an unreal or imagined situation. The speaker is not simply checking the price; they are expressing a wish about a situation that is not true right now.

Så dyr means so expensive or that expensive, depending on how you translate it into natural English.

So:

• den er dyr = it is expensive
• den er så dyr = it is so expensive / that expensive
• den ikke var så dyr = it were not so expensive / it were not that expensive

With ikke, the idea is that the price is higher than the speaker would like.

It is mainly a wish, not a direct request.

Jeg ville gerne have ... can sometimes sound polite, but here, because it is followed by hvis den ikke var så dyr, it is clearly expressing a personal wish about a hypothetical situation.

So the sentence is closer to:

• I would like one, if it were not so expensive

rather than:

• I would like to order one

The tone is natural, conversational, and slightly tentative.