Jeg vil gerne forstå teksten ordentligt, før jeg afleverer opgaven.

Not literally in natural English, no. In Danish, gerne often means gladly / willingly / with pleasure, but together with vil it very often works like would like to.

So:

• Jeg vil forstå teksten = I want to understand the text
  
  • more direct, sometimes a bit blunt
• Jeg vil gerne forstå teksten = I would like to understand the text
  
  • softer and more natural in many situations

A native English speaker should think of vil gerne as a very common polite pattern, not as a word-for-word match.

Because vil is a modal verb, and modal verbs in Danish normally take the bare infinitive.

So you say:

• jeg vil forstå
• jeg kan forstå
• jeg skal forstå

not:

• jeg vil at forstå

This is similar to English:

• I want to understand
• I can understand

not:

• I can to understand

So after vil, forstå stays in the infinitive without at.

Because teksten means the text.

In Danish, the definite article is often attached to the end of the noun:

• en tekst = a text
• teksten = the text

That is one of the biggest structural differences from English. Instead of putting the before the noun, Danish often adds -en, -et, or -ne to the noun.

Here, teksten makes sense because it refers to a specific text the speaker is dealing with.

For the same reason as teksten: it is the definite form.

• en opgave = an assignment / a task
• opgaven = the assignment

So jeg afleverer opgaven means I hand in the assignment or I submit the assignment.

In this sentence, the speaker is talking about a specific assignment, not just any assignment.

Here ordentligt means something like:

• properly
• correctly
• thoroughly

So forstå teksten ordentligt means understand the text properly / thoroughly.

The -t form is used because ordentligt is functioning as an adverb here. It describes how the speaker wants to understand the text.

Compare:

• en ordentlig forklaring = a proper explanation
  
  • adjective
• forstå det ordentligt = understand it properly
  
  • adverb

This word can be a little tricky because English learners may expect something closer to orderly, but in this sentence properly or thoroughly is the right idea.

Because that is the natural Danish word order here.

In forstå teksten ordentligt, the object comes first:

• teksten = the object

and then the adverb describing the manner:

• ordentligt = properly

This is very normal in Danish. Compare:

• læse bogen grundigt = read the book thoroughly
• forklare det tydeligt = explain it clearly
• forstå teksten ordentligt = understand the text properly

If you try to place ordentligt earlier, it will often sound less natural or create a different emphasis.

Because før jeg afleverer opgaven is a subordinate clause, and the sentence is using a comma before it.

However, this is a point where Danish punctuation can vary. In modern Danish, the so-called start comma before subordinate clauses is optional, depending on the comma system a writer follows.

So both of these can be seen:

• Jeg vil gerne forstå teksten ordentligt, før jeg afleverer opgaven.
• Jeg vil gerne forstå teksten ordentligt før jeg afleverer opgaven.

The version with the comma is completely normal. It simply marks the subordinate clause more clearly.

Because før introduces a subordinate clause, and subordinate clauses in Danish usually do not use the main-clause verb-second pattern.

So after før, the normal order is:

• før jeg afleverer opgaven
• conjunction + subject + verb + object

Compare:

• Main clause: Jeg afleverer opgaven i morgen.
• Subordinate clause: før jeg afleverer opgaven

A learner often notices Danish verb-second word order in main clauses, but subordinate clauses are different. After words like før, fordi, hvis, når, and at, the subject usually comes before the finite verb.

Because Danish often uses the present tense for future meaning when the time is already clear from context.

Here, før already shows that this is about a future point:

• før jeg afleverer opgaven = before I hand in the assignment

This is very similar to English, which also often uses the present tense after time words:

• before I hand in the assignment
• when I arrive
• after she finishes

So the Danish present tense here is completely normal.

Here aflevere means hand in or submit.

It can be used for giving something over officially or returning something to someone:

• aflevere en opgave = hand in/submit an assignment
• aflevere en bog = return a book
• aflevere nøglerne = hand in the keys

So in a school or university context, aflevere opgaven is a very common expression for submit the assignment.

Here it simply means before in a time sense.

It introduces the action that happens later:

• first: understand the text properly
• then: hand in the assignment

So the structure is:

• main clause: Jeg vil gerne forstå teksten ordentligt
• subordinate clause: før jeg afleverer opgaven

A useful thing to remember is that før commonly introduces a time clause, and that is why the present tense and subordinate-clause word order both appear here.