Jeg vil gerne høre interviewet i radioen i aften.

Gerne is a very common Danish word that often adds the idea of gladly, with pleasure, or would like to.

In this sentence, jeg vil gerne høre... is best understood as I would like to hear/listen to...

So:

• jeg vil høre = I want to hear
• jeg vil gerne høre = I would like to hear

It makes the sentence sound softer and more natural.

Here, vil is closer to want to or, more politely with gerne, would like to.

Danish ville / vil can sometimes express future meaning, but in this sentence it is mainly about desire or intention, not simple future.

So Jeg vil gerne høre interviewet i radioen i aften means something like:

• I’d like to hear the interview on the radio tonight
• not just I will hear the interview...

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

So you get:

• jeg vil høre
• jeg kan høre
• jeg skal høre

not:

• jeg vil at høre

This is similar to English:

• I will hear
• I can hear

not I will to hear

That is a very common question.

Høre basically means hear, but in many contexts it can also be used where English would naturally say listen to, especially with radio, music, interviews, and similar things.

• høre interviewet = hear/listen to the interview

Lytte is more specifically listen, with an emphasis on actively paying attention, and it usually takes til:

• lytte til interviewet

So both can work, but the nuance is a little different:

• høre interviewet = hear/listen to the interview
• lytte til interviewet = listen to the interview attentively

Because interviewet is the definite form: the interview.

Danish usually adds the definite article to the end of the noun:

• et interview = an interview
• interviewet = the interview

This sentence is talking about a specific interview, presumably one already known from context.

For the same reason: it is the definite form of radio.

• en radio = a radio
• radioen = the radio

So i radioen literally looks like in the radio, but idiomatically it means on the radio.

Also notice that radio is a common gender noun, so it takes en in the indefinite form and -en in the definite form.

This is just an idiomatic difference between the two languages.

English uses on for media like radio and TV:

• on the radio
• on TV

Danish often uses i in these expressions:

• i radioen
• i fjernsynet
• i tv

So you should not translate the preposition too literally. Here i radioen simply means on the radio.

I aften means tonight or this evening, depending on context.

In this sentence, it means that the listening will happen later the same day, during the evening.

Compare:

• i aften = tonight / this evening
• om aftenen = in the evening / in the evenings more generally
• i morgen aften = tomorrow evening

So i aften is a fixed and very common time expression.

That is normal Danish sentence structure.

The sentence is built like this:

• Jeg = subject
• vil = modal verb
• gerne = adverb
• høre = infinitive
• interviewet = object
• i radioen = adverbial of medium/place
• i aften = adverbial of time

A very natural pattern in Danish is:

subject + finite verb + adverb + infinitive + object + other information

Time expressions often come late in the sentence, so i aften at the end sounds very natural.

Yes. Danish often moves another element to the front for emphasis, but then the verb must stay in second position.

For example:

• Jeg vil gerne høre interviewet i radioen i aften.
• I aften vil jeg gerne høre interviewet i radioen.

Both are correct. The second version puts extra focus on tonight.

This is an important Danish rule: in main clauses, the finite verb usually stays in second position.

Yes, a few things:

• vil gerne often corresponds to English would like to
• modal verbs like vil are followed by an infinitive without at
• Danish uses a suffixed definite article:
  • interviewet = the interview
  • radioen = the radio
• i radioen means on the radio
• høre can cover both hear and, in some contexts, listen to

So even though the sentence is not difficult, it contains several very typical Danish patterns.