Jeg lægger en flaske vand i min cykelkurv, før jeg cykler til arbejdet.

Both lægger and cykler are present-tense forms.

In Danish, the present tense is often used for:

• habits / routines: I put a bottle of water in my bike basket before I cycle to work
• near-future actions: something you are about to do

So this sentence most naturally sounds like a usual routine. English can do something similar with the present simple: I put ... before I cycle ...

Because lægge and ligge work like a very common Danish pair:

• lægge = to lay / put something somewhere
  
  • it usually takes an object
• ligge = to lie / be lying somewhere
  
  • it describes where something is

So:

• Jeg lægger en flaske vand i min cykelkurv = I put a bottle of water in my bike basket
• En flaske vand ligger i min cykelkurv = A bottle of water is lying in my bike basket

A useful shortcut:

• lægge = the action of placing
• ligge = the result/location

Also, Danish often uses more specific placement verbs than English. With a bottle, some speakers might also say stiller if they imagine the bottle standing upright. Lægger suggests laying/placing it in the basket.

This is a very common Danish pattern with containers and amounts.

• en flaske vand = a bottle of water
• et glas mælk = a glass of milk
• en kop kaffe = a cup of coffee

Danish often leaves out a separate word for of in these expressions.

You can also say:

• en flaske med vand = a bottle with water in it

But that sounds a bit different:

• en flaske vand focuses on the quantity/type
• en flaske med vand focuses more on the bottle containing water

Also note:

• en vandflaske usually means a water bottle as an object/container, not necessarily emphasizing the amount inside it

Because Danish usually writes compound nouns as one word.

Here:

• cykel = bike
• kurv = basket
• cykelkurv = bike basket

This is very normal in Danish:

• arbejdsdag = workday
• sommerferie = summer holiday
• kaffekop = coffee cup

A useful rule: in Danish compounds, the last part is the main noun. So in cykelkurv, the main noun is kurv.

That matters for grammar too:

• en kurv
• en cykelkurv
• cykelkurven = the bike basket

There are two things going on here.

1) Why min and not mit?
Because cykelkurv is a common-gender noun.

• en cykelkurv
• therefore: min cykelkurv

Compare:

• mit hus because hus is et hus
• min bog because bog is en bog

2) Why not min cykelkurven?
Because after a possessive like min, Danish normally uses the indefinite form of the noun:

• min cykelkurv
• mit arbejde
• mine sko

So Danish normally does not combine a possessive with the definite ending here.

Because i means in/inside, and a basket is treated as something you put an item inside.

• i min cykelkurv = in my bike basket

If you used på, it would usually mean on something rather than inside it.

Compare:

• i kurven = in the basket
• på cyklen = on the bike

So:

• i min cykelkurv = inside the basket attached to the bike

Because før introduces a subordinate clause, and Danish word order changes in subordinate clauses.

In a main clause, Danish usually has verb-second word order:

• Jeg cykler til arbejdet

But after a subordinating word like før, the clause keeps normal subject + verb order:

• før jeg cykler til arbejdet

So:

• før jeg cykler ... is correct
• før cykler jeg ... is not correct here

A useful comparison:

• Jeg lægger en flaske vand i min cykelkurv, før jeg cykler til arbejdet.
• Før jeg cykler til arbejdet, lægger jeg en flaske vand i min cykelkurv.

Notice that when the før-clause comes first, the main clause changes to:

• lægger jeg not
• jeg lægger

That is normal Danish inversion in the main clause.

Because Danish has had two accepted comma styles.

With start comma, you put a comma before a subordinate clause:

• ..., før jeg cykler til arbejdet

Without start comma, you usually do not:

• ... før jeg cykler til arbejdet

So the comma in your sentence is not a grammar mistake. It reflects one accepted Danish comma system.

Før means before in time.

So:

• før jeg cykler til arbejdet = before I cycle to work

It introduces the action that happens later. The order of events is:

1. Jeg lægger en flaske vand i min cykelkurv
2. jeg cykler til arbejdet

Yes, and this is a very useful nuance.

• til arbejdet = to the workplace / to the job in a more definite sense
• til arbejde = to work
• på arbejde = to work / at work, depending on context

Many Danish speakers would very naturally say:

• før jeg cykler til arbejde or
• før jeg cykler på arbejde

So the version with til arbejdet is understandable and grammatical, but til arbejde or på arbejde may sound more idiomatic when talking about the everyday commute in general.

Because arbejde is a neuter noun (et-word), and -et is the definite singular ending.

So:

• et arbejde = a job / a piece of work
• arbejdet = the work / the job

In this sentence, arbejdet refers to work as the destination.

A quick pattern:

• en bog → bogen
• et hus → huset
• et arbejde → arbejdet

Most naturally, it sounds like a routine or repeated action.

That is because:

• the verbs are in the present tense
• the sentence describes a typical sequence: first this, then that

So it sounds like:

• This is what I do before I cycle to work

If you wanted to describe one specific past event, you would use past tense:

• Jeg lagde en flaske vand i min cykelkurv, før jeg cyklede til arbejdet.