Jeg lægger brevet i en kuvert og skriver både afsender og modtager tydeligt på forsiden.

Because lægge means to lay / to put something somewhere, while ligge means to lie / to be located.

• Jeg lægger brevet i en kuvert = I put the letter in an envelope
• Brevet ligger i en kuvert = The letter is in an envelope

A useful shortcut:

• lægge = usually takes an object, because you put something
• ligge = describes where something is

So here, since jeg am actively putting brevet somewhere, lægger is correct.

Because brevet is the definite form of brev.

• et brev = a letter
• brevet = the letter

In Danish, the definite article is often added to the end of the noun instead of being a separate word like English the.

So:

• brev = letter
• brevet = the letter

Because the letter goes inside the envelope, so Danish uses i = in.

• i en kuvert = in an envelope

If you used på, it would mean on the envelope, which would not fit this part of the sentence.

Later in the sentence, you do get på forsiden, because the sender and recipient are written on the front side.

Danish nouns have grammatical gender, and the indefinite article depends on that:

• en for common gender nouns
• et for neuter nouns

Here:

• et brev = a letter
• en kuvert = an envelope

This is something you usually have to learn with each noun.

Because Danish, like English, often leaves out the subject in the second part of a coordinated sentence when it is the same subject.

So:

• Jeg lægger brevet i en kuvert og skriver ... means
• I put the letter in an envelope and write ...

You could repeat jeg, but it is usually unnecessary here:

• Jeg lægger brevet i en kuvert, og jeg skriver ...

Both are possible, but the version without the second jeg sounds more natural in a simple sentence like this.

Både ... og ... means both ... and ...

So:

• både afsender og modtager = both the sender and the recipient

It is a very common structure in Danish.

Examples:

• Jeg kan både læse og skrive dansk. = I can both read and write Danish.
• Hun drikker både te og kaffe. = She drinks both tea and coffee.

Because Danish often leaves out articles in contexts where English might use the or the name/address of the sender and recipient.

Here, afsender and modtager are being used in a practical, label-like way:

• skriver både afsender og modtager tydeligt
  = write both sender and recipient clearly

In natural English, you might translate it more smoothly as:

• I clearly write both the sender and the recipient on the front or
• I clearly write the sender’s and recipient’s details on the front

So the missing article is normal Danish usage here.

Because tydeligt is an adverb here, not an adjective.

• tydelig = clear (adjective)
• tydeligt = clearly (adverb)

It describes how the person writes:

• skriver tydeligt = writes clearly

This -t often appears when an adjective is used adverbially in Danish.

Compare:

• en tydelig adresse = a clear address
• jeg skriver tydeligt = I write clearly

Forsiden means the front side or the front.

It is the definite form of forside:

• en forside = a front side / front page / front
• forsiden = the front side / the front

In this sentence, it refers to the front of the envelope:

• på forsiden = on the front

That is a natural place in Danish for an adverbial phrase of location.

The structure is roughly:

• Jeg = subject
• lægger / skriver = verbs
• brevet / både afsender og modtager = objects
• i en kuvert / tydeligt / på forsiden = extra information

So på forsiden comes late because it tells you where the writing happens.

You could think of it as:

• I put the letter in an envelope and write both sender and recipient clearly on the front.

Literally, it may look that way, but in real usage it means you write the sender and recipient information, such as names and addresses.

This is common shorthand in Danish. Native speakers understand that it refers to the relevant details, not the people themselves.

So the idea is:

• write the sender’s details
• write the recipient’s details

Because Danish uses the present tense just like English for:

• actions happening now
• habits or routines
• instructions in a straightforward style

So Jeg lægger ... og skriver ... can mean:

• I am putting ... and writing ...
• I put ... and write ...
• When I mail a letter, I put ... and write ...

The exact meaning depends on context.

The basic pattern is:

• Jeg = subject
• lægger = verb
• brevet = object
• i en kuvert = place/direction
• og skriver = second coordinated verb
• både afsender og modtager = object
• tydeligt = manner
• på forsiden = place

So a rough breakdown is:

Jeg | lægger | brevet | i en kuvert | og | skriver | både afsender og modtager | tydeligt | på forsiden

This is normal Danish main-clause word order: the finite verb comes early, and the rest follows in a fairly flexible but natural order.

Yes, in many contexts you could say på kuverten = on the envelope, but it is slightly less specific.

• på kuverten = on the envelope
• på forsiden = on the front side

In this sentence, på forsiden is more precise, because addresses are typically written on the front of the envelope, not just anywhere on it.

Here are the main ones:

• jeg = I
• lægger → infinitive lægge = to put, to lay
• brevet → noun brev = letter
• i = in
• en kuvert = an envelope
• skriver → infinitive skrive = to write
• både ... og ... = both ... and ...
• afsender = sender
• modtager = recipient
• tydeligt → adjective tydelig = clear
• forsiden → noun forside = front side, front

Knowing the dictionary forms helps a lot when you look words up or try to build similar sentences yourself.