Jeg kører grene og gammelt græs ud i komposten med trillebøren, før det begynder at regne.

Yes, køre often means to drive, but it also has a broader meaning: to transport or move something on wheels.

In this sentence, Jeg kører grene og gammelt græs ... med trillebøren means that the speaker is moving the branches and old grass using a wheelbarrow. So in natural English, it is more like:

• I wheel the branches and old grass...
• I take the branches and old grass... in the wheelbarrow
• I transport the branches and old grass...

So kører does not have to involve a car.

Because græs is a neuter noun in Danish: et græs.

When an adjective comes before a singular neuter noun in the indefinite form, it usually gets -t:

• en gammel stol
• et gammelt hus
• et gammelt græs would be structurally possible, but with græs as a mass noun, you normally just say gammelt græs

So:

• gammelt agrees with græs
• gamle would be used for plural or definite forms, for example:
  • de gamle grene
  • det gamle græs

Because Danish often leaves nouns indefinite and article-less when speaking generally about some amount of something.

Here:

• grene = branches
• gammelt græs = old grass

This sounds natural because the speaker is not talking about one specific branch or one specific piece of grass, but just some branches and some old grass.

Compare:

• Jeg kører grene og gammelt græs ud... = I’m taking branches and old grass out...
• Jeg kører grenene og det gamle græs ud... = I’m taking out the branches and the old grass...
  This would mean specific branches and specific old grass already known in the context.

Because komposten means the compost or more naturally the compost heap/bin, referring to a specific compost that both speaker and listener know about.

In Danish, the definite article is usually added to the end of the noun:

• en kompost = a compost / compost heap
• komposten = the compost / the compost heap

So ud i komposten means the material is going into a specific compost area.

Ud i combines two ideas:

• ud = out
• i = into / in

Together, they suggest movement outward and into something. In this sentence, the speaker is moving the branches and grass outward from where they are now and into the compost.

So:

• ud gives the sense of direction away from the current place
• i komposten gives the destination

That is why ud i komposten feels stronger and more specific than just i komposten.

A related point:

• ud til komposten would mean more like out to the compost
• ud i komposten means out into the compost

Med trillebøren means using the wheelbarrow as the means or tool.

So the focus is on how the speaker is transporting the material.

• med trillebøren = with the wheelbarrow / by wheelbarrow

You could also sometimes hear i trillebøren, but that would focus more on where the branches and grass are physically placed:

• i trillebøren = in the wheelbarrow

So the difference is roughly:

• med trillebøren = using the wheelbarrow
• i trillebøren = located in the wheelbarrow

In this sentence, med trillebøren is very natural.

Trillebør means wheelbarrow, and trillebøren means the wheelbarrow.

It is a common noun in gardening and yard work.

Forms:

• en trillebør = a wheelbarrow
• trillebøren = the wheelbarrow

So med trillebøren means with the wheelbarrow.

Here, det does not refer to a specific thing. It is a dummy subject, just like English it in:

• It is raining
• It starts to rain

Danish weather expressions often use det in the same way:

• Det regner = It is raining
• Det sner = It is snowing
• Det begynder at regne = It starts to rain

So det is required by the grammar, even though it does not point to an actual object.

After begynde, Danish normally uses at before the infinitive:

• begynde at regne = begin to rain
• begynde at arbejde = begin to work
• begynde at spise = begin to eat

Here at works very much like English to in to rain.

So:

• det begynder at regne = it begins to rain / it starts to rain

Danish uses the simple present much more broadly than English does.

So Jeg kører ... can mean:

• I drive / transport ...
• I am taking ...
• I’m wheeling ...

depending on context.

Likewise, det begynder at regne means it starts to rain or it is about to start raining, depending on the situation.

English often prefers the progressive form I’m taking, but Danish usually just uses the present tense:

• Jeg kører ... not necessarily
• Jeg er ved at køre ...

The sentence is completely normal Danish.

After før, you have a subordinate clause, and Danish subordinate clauses usually keep the order subject + verb:

• før det begynder at regne

That is why it is:

• det begynder not
• begynder det

If you put the før-clause first, then the main clause changes because Danish uses inversion in main clauses after a fronted element:

• Før det begynder at regne, kører jeg grene og gammelt græs ud i komposten med trillebøren.

So:

• subordinate clause: før det begynder at regne
• main clause after fronting: kører jeg

That word order difference is very important in Danish.

The comma before før is normal and correct here because før det begynder at regne is a subordinate clause.

However, Danish comma rules allow some variation depending on the comma system being used. So you may also see the sentence written without that comma in some contexts.

With the comma:

• Jeg kører ... med trillebøren, før det begynder at regne.

Without the comma:

• Jeg kører ... med trillebøren før det begynder at regne.

Both can be encountered, but the version with the comma is very common and easy for learners to parse.

Yes, it is natural Danish.

A native speaker might also choose slightly different wording depending on exactly what they mean:

• Jeg kører grene og gammelt græs ud til komposten med trillebøren...
  This emphasizes going out to the compost.

• Jeg kører grene og gammelt græs i trillebøren ud til komposten...
  This emphasizes that the material is in the wheelbarrow.

• Jeg kører grene og gammelt græs ud i komposten...
  This emphasizes movement out and into the compost.

So the original sentence is good, but small changes can shift the focus slightly.