Hun skal til at begynde sin arbejdsdag, men først drikker hun en kop kaffe.

The pattern skal til at + infinitive means is about to + verb or is just going to + verb.

So:

• Hun skal til at begynde sin arbejdsdag = She is about to start her workday

Here, skal does not mean a strong must. It often shows that something is imminent or about to happen.

Compare:

• Hun begynder sin arbejdsdag = She starts her workday
• Hun skal til at begynde sin arbejdsdag = She is about to start her workday

The second version gives a clearer sense that the action has not started yet, but is very close.

Danish uses sin/sit/sine when the possessor is the same as the subject of the clause.

Here:

• Hun = the subject
• sin arbejdsdag = her own workday

Because it is her workday, belonging to the same person as hun, Danish uses the reflexive possessive sin.

A useful contrast:

• Hun begynder sin arbejdsdag = She starts her own workday
• Hun begynder hendes arbejdsdag = She starts another woman’s workday

Also, the form changes with gender and number:

• sin for common gender singular
• sit for neuter singular
• sine for plural

Since arbejdsdag is a common-gender singular noun, sin is the correct form.

Because the possessive already fills that role.

In Danish, a possessive like min, din, sin, vores, etc. normally replaces the article. So you say:

• sin arbejdsdag = her workday
• not sin en arbejdsdag

This works much like English:

• her workday
• not her a workday

So the absence of an article is completely normal here.

Danish, like German, very often makes compound nouns by joining words together.

So:

• arbejde = work
• dag = day
• arbejdsdag = workday

The -s- in the middle is a common linking element in Danish compounds. It does not always translate as anything by itself; it just helps form the compound naturally.

Other examples:

• arbejdsplads = workplace
• fødselsdag = birthday
• mandag = Monday

For English speakers, this is important because English often writes such expressions as two words, while Danish often prefers one compound word.

This is because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

After men, a new main clause begins. If først is placed first for emphasis, then the verb must come next:

• men først drikker hun en kop kaffe

Structure:

• først = first position
• drikker = second position
• hun = after the verb

This is very standard Danish word order.

You can also say:

• men hun drikker først en kop kaffe

That is also grammatical, but the emphasis is slightly different.
With først in first position, the sentence highlights the sequence more strongly: but first...

Here først means first or before that.

It shows the order of actions:

1. she drinks a cup of coffee
2. then she starts her workday

So in this sentence, først signals that the coffee happens before the workday begins.

It can also appear in other contexts, for example:

• Først spiser vi, så går vi. = First we eat, then we go.
• Jeg kommer først i morgen. = I’m only coming tomorrow / not until tomorrow.

So the exact translation depends on context, but in your sentence it is clearly about sequence.

En kop kaffe literally means a cup of coffee.

This is a very common measure expression in Danish:

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

Notice that kaffe does not need its own article here. The article belongs to kop:

• en
  • kop
• then kaffe tells you what kind of cup it is

So the structure is similar to English: a cup of coffee.

In everyday speech, Danes may also say en kaffe in some contexts, meaning a coffee, but en kop kaffe is more literal and neutral.

Drikker is the present tense of drikke.

Danish often uses the present tense in descriptions, routines, and sequences of events, especially when the context already makes the timing clear.

So here:

• Hun skal til at begynde sin arbejdsdag sets up the situation
• men først drikker hun en kop kaffe describes what happens first

Even though the first part has a kind of about to meaning, the second clause stays in the present tense because it is simply describing the action in a natural, immediate way.

This is very normal in Danish. English sometimes does something similar:

• She’s about to start work, but first she drinks a cup of coffee.

Even if English might more often choose has or will have in some contexts, Danish present tense is perfectly natural here.

Yes, men here simply means but.

It connects the two ideas:

• she is about to start her workday
• but before that, she drinks coffee

So it introduces a contrast or interruption in the expected sequence. You might expect her to start work immediately, but instead she first has coffee.

Grammatically, men also matters because it introduces a new main clause, which is why normal Danish main-clause word order applies after it:

• men først drikker hun...