Jeg vil udskrive en kopi af dokumentet, før jeg går hjem fra universitetet.

Because after a modal verb like vil, Danish normally uses the bare infinitive without at.

• jeg vil udskrive = I want to print / I will print
• not jeg vil at udskrive

This is similar to English:

• I want to print
• but I will print, not I will to print

Common Danish modal verbs that work this way include:

• vil = will / want to
• kan = can
• skal = shall / must / am going to
• må = may / must

So vil + infinitive is the normal pattern here.

Vil can mean either will or want to, depending on context.

In this sentence, it often feels closer to:

• I want to print a copy...
• or I’m going to print a copy...

It can express intention, not just simple future tense.

That is very common in Danish. Danish often uses present tense or verbs like vil to talk about the future, rather than having a special future form like English does.

So here, vil suggests that the speaker intends or wants to do the action before going home.

Udskrive is the verb to print out / to print.

It is built from:

• ud- = out
• skrive = write

So historically it is something like write out, but in modern usage it commonly means print out, especially for documents.

It is written as one word in Danish:

• udskrive

Unlike German, Danish does not usually split this kind of verb apart in the same way. So you get forms like:

• jeg udskriver dokumentet = I print the document
• jeg vil udskrive dokumentet = I want to print the document
• jeg har udskrevet dokumentet = I have printed the document

Because kopi is a common-gender noun in Danish, so it takes en.

• en kopi = a copy

Danish nouns are usually either:

• common gender → en
• neuter → et

So you simply have to learn the noun with its article:

• en kopi
• et dokument

That is why the sentence has:

• en kopi
• dokumentet

since dokument is a different noun with a different gender.

Because dokumentet is the definite form: the document.

Danish usually adds the definite article as an ending on the noun:

• et dokument = a document
• dokumentet = the document

So in the phrase:

• en kopi af dokumentet

you get:

• a copy of the document

This is one of the most important Danish patterns:

• en bog → bogen
• et hus → huset
• et dokument → dokumentet

Because af is the normal preposition here for of.

• en kopi af dokumentet = a copy of the document

This is a very common structure in Danish:

• toppen af bjerget = the top of the mountain
• slutningen af filmen = the end of the film
• en del af arbejdet = part of the work

So if an English speaker is thinking of, Danish often uses af.

Because før jeg går hjem fra universitetet is a subordinate clause, and Danish commonly places a comma before subordinate clauses.

So the sentence is divided like this:

• Jeg vil udskrive en kopi af dokumentet
• før jeg går hjem fra universitetet

The second part depends on the first part, so the comma marks that boundary.

In modern Danish comma practice, this kind of comma is very standard and helpful for reading.

Because after a subordinating conjunction like før (before), Danish normally uses subordinate clause word order, where the subject comes before the finite verb:

• før jeg går
• not før går jeg

Compare:

• Main clause: Jeg går hjem.
• Subordinate clause: ...før jeg går hjem.

This is important because Danish main clauses often have verb-second word order, but subordinate clauses do not work the same way.

So after words like:

• at = that
• fordi = because
• når = when
• hvis = if
• før = before

you usually get normal subject + verb order.

Literally, går means walks/goes, but gå hjem is a very common Danish expression meaning go home.

So:

• jeg går hjem = I go home / I’m going home

It does not always mean that you are physically walking. It can simply mean returning home in general.

This is similar to some English uses where go home does not specify the method of travel.

Because hjem already contains the idea of movement to home.

So Danish says:

• jeg går hjem = I go home

not:

• jeg går til hjem

This is very natural and very common. Compare:

• jeg tager hjem = I’m going home
• vi kører hjem = we drive home

But if you are talking about being at home rather than moving there, Danish uses:

• hjemme = at home

So the contrast is:

• hjem = to home / homeward
• hjemme = at home

Because universitetet is the definite form: the university.

• et universitet = a university
• universitetet = the university

In this sentence, the speaker means a specific university they are leaving from, so the definite form sounds natural:

• fra universitetet = from the university

English often uses the here, and Danish does the same idea by adding -et to the noun.

Because fra is the normal preposition for movement or origin meaning from.

• jeg går hjem fra universitetet = I go home from the university

Af would not work here, because af usually means things like:

• of
• by
• sometimes from in other special contexts

But when leaving a place or indicating where someone comes from physically, Danish usually uses fra.

Examples:

• fra skolen = from school
• fra kontoret = from the office
• fra universitetet = from the university

Yes. This sentence is already natural, but Danish often allows small variations depending on style and context.

For example:

• Jeg vil udskrive en kopi af dokumentet, før jeg tager hjem fra universitetet.
• Jeg vil printe en kopi af dokumentet, før jeg går hjem fra universitetet.

A few notes:

• tage hjem is also very common for go home
• printe is a common modern loanword meaning print
• udskrive sounds slightly more formal or standard in some contexts

So the original sentence is perfectly good, but it is not the only possible natural wording.