Jeg ville gerne gå i biografen i aften, hvis jeg ikke var så træt.

Ville is the past form of vil in a purely grammatical sense, but in sentences like this it often works like English would, not simple past wanted.

So:

• Jeg vil gerne gå i biografen i aften = I would like / want to go to the cinema tonight
• Jeg ville gerne gå i biografen i aften, hvis ... = I would like to go to the cinema tonight, if ...

Here ville helps create a hypothetical or less direct meaning. The speaker is talking about something they would do under different circumstances, not about a past event.

Gerne is a very common Danish word. It often means something like:

• gladly
• with pleasure
• like to

In ville gerne, the combination is usually translated as would like to.

So:

• Jeg ville gerne gå ... = I would like to go ...

You should not translate gerne too literally every time. In many cases, it is part of a natural Danish way of expressing desire or willingness.

Because ville is a modal verb, and modal verbs in Danish are followed by the infinitive without at.

So:

• jeg vil gå
• jeg kan gå
• jeg skal gå
• jeg må gå
• jeg ville gerne gå

Not:

• jeg ville gerne at gå

That would be wrong in standard Danish.

In Danish, the normal expression for going to the cinema is gå i biografen.

Literally, it looks like go in the cinema, but idiomatically it means go to the cinema / go to the movies.

This is just the standard Danish expression, so it is best learned as a chunk:

• gå i biografen = go to the cinema
• være i biografen = be at/in the cinema

English and Danish do not always use the same prepositions, so this is a good phrase to memorize as a whole.

Biografen is the definite form: the cinema.

Danish often uses the definite form in places where English might say:

• to the cinema
• to the movies

So i biografen is the normal idiomatic phrase.

Compare:

• en biograf = a cinema
• biografen = the cinema

In this sentence, biografen does not necessarily mean one specific cinema already mentioned. It is simply the normal way to express the activity.

Because i aften is the normal Danish expression meaning this evening / tonight.

It is written as two words:

• i aften = tonight
• i morgen = tomorrow
• i dag = today

So this is something you should learn as a fixed time expression.

Hvis means if.

It introduces the condition:

• hvis jeg ikke var så træt = if I were not so tired

So the whole sentence has a conditional structure:

• main idea: Jeg ville gerne gå i biografen i aften
• condition: hvis jeg ikke var så træt

This is very similar to English I would like to go to the cinema tonight if I weren’t so tired.

Because in a subordinate clause introduced by hvis, Danish word order changes.

In a main clause, the negative word ikke usually comes after the finite verb:

• Jeg var ikke træt

But in a subordinate clause, ikke usually comes before the finite verb:

• hvis jeg ikke var så træt

So this is a very important pattern:

• main clause: Jeg kommer ikke
• subordinate clause: ..., fordi jeg ikke kommer

That is exactly what happens here.

Because this sentence describes an unreal or hypothetical situation.

The speaker is tired, so going to the cinema is not really happening. Danish often uses a past form in this kind of conditional sentence, just like English often says:

• if I were not so tired
• if I wasn’t so tired

So:

• hvis jeg ikke var så træt = if I were not so tired

Even though the meaning is about the present situation, the past form var helps mark it as hypothetical.

Så means so here, and træt means tired.

So:

• så træt = so tired

This is the normal Danish pattern for this kind of emphasis:

• så god = so good
• så dyr = so expensive
• så træt = so tired

In this sentence, it means the speaker is tired to a degree that affects what they would like to do.

It is more like I would like to go.

Even though ville is historically the past form, here it does not primarily mean a past wish. It expresses a present hypothetical desire.

So the natural meaning is:

• I would like to go to the cinema tonight, if I weren’t so tired

If you wanted to say a real past meaning such as I wanted to go, the context would need to make that clear.

Yes, you could, but it changes the feeling slightly.

• Jeg vil gerne gå ... hvis jeg ikke er så træt sounds more like a real future possibility: I want/would like to go ... if I’m not too tired
• Jeg ville gerne gå ... hvis jeg ikke var så træt sounds more hypothetical: I would like to go ... if I weren’t so tired

So the original sentence suggests that the speaker probably is tired right now, and that is the obstacle.

In natural speech, several words may sound more reduced than you might expect from the spelling.

A rough learner-friendly approximation is:

yai VIL-uh GERN-uh goh i byo-GRAH-fen i AF-ten, vis yai ik-ke va so tret

A few useful notes:

• jeg often sounds closer to yai
• gerne is often pronounced roughly like ger-nə
• ikke is often pronounced ik-ke
• var is often pronounced more like va
• træt has a vowel sound English does not have exactly, so it takes practice

The exact pronunciation varies by speaker and region, but those reductions are very common.