Jeg lægger nøglen på bordet ved døren.

This is one of the most important verb pairs in Danish.

• at lægge = to lay / to put something somewhere
• at ligge = to lie / to be located somewhere

In your sentence, the subject is actively moving the key to a place, so Danish uses lægger.

• Jeg lægger nøglen på bordet. = I put the key on the table.
• Nøglen ligger på bordet. = The key is lying/is on the table.

A useful shortcut:

• if there is a direct object, Danish often uses lægge
• if something is already in a place, Danish often uses ligge

Here, nøglen is the object, so lægger is correct.

Lægger is the present tense of at lægge.

Common forms:

• infinitive: at lægge
• present: lægger
• past: lagde
• past participle: lagt

So:

• Jeg lægger nøglen ... = I am putting / I put the key ...

In Danish, the present tense is often used where English might say either put or am putting, depending on context.

Because nøglen is the definite form: the key.

Danish usually puts the definite article at the end of the noun instead of using a separate word like English the.

For this noun:

• en nøgle = a key
• nøglen = the key

So the -en ending means the.

This is very common in Danish:

• en stol → stolen = the chair
• en dør → døren = the door

For the same reason: they are also in the definite form.

• et bord = a table

• bordet = the table

• en dør = a door
• døren = the door

Danish nouns have grammatical gender, and that affects the definite ending:

• common gender nouns usually take -en
• neuter nouns usually take -et

So in this sentence:

• nøglen = the key
• bordet = the table
• døren = the door

Because in Danish, the normal definite article is usually a suffix attached to the noun.

English:

• the key
• the table
• the door

Danish:

• nøglen
• bordet
• døren

This is one of the biggest differences from English. Danish does have separate demonstrative words like den and det, but in an ordinary sentence like this, the definite ending is the normal choice.

Here, på means on.

So:

• på bordet = on the table

With lægge, på often marks the surface or place where something is being put:

• Jeg lægger bogen på stolen. = I put the book on the chair.
• Hun lægger telefonen på bordet. = She puts the phone on the table.

In many contexts, på can correspond to English on, but prepositions do not always match perfectly between Danish and English, so it is best to learn them in phrases.

In this sentence, it can naturally be understood as the destination of the movement: onto the table / on the table.

Danish often uses på in both kinds of situations:

• location: Bogen ligger på bordet. = The book is on the table.
• movement toward placement: Jeg lægger bogen på bordet. = I put the book on the table.

English sometimes makes a clearer distinction between on and onto, but Danish often just uses på.

Ved døren means by the door, near the door, or at the door, depending on context.

• ved = by / near / at
• døren = the door

So bordet ved døren means the table by the door.

In this sentence, ved døren describes which table you mean: the one near the door.

Ved is a preposition. Here it connects bordet and døren.

The structure is:

• på bordet = on the table
• ved døren = by the door

Together:

• på bordet ved døren = on the table by the door

So ved døren works like an extra description of bordet.

Most naturally, it describes the table.

So the sentence is understood as:

• I put the key [on the table [by the door]].

In other words, it is not usually understood as I put the key by the door on the table. The phrase ved døren most naturally attaches to bordet.

If you wanted to emphasize a different relationship, Danish would often restructure the sentence.

This is a very normal Danish main-clause word order:

• Jeg = subject
• lægger = finite verb
• nøglen = direct object
• på bordet ved døren = place expression

So the pattern is basically:

Subject + verb + object + adverbial/place phrase

This is very similar to English:

• I put the key on the table by the door.

Danish word order becomes more noticeably different when another element is placed first:

• På bordet ved døren lægger jeg nøglen.

Then the verb still has to come second. That is a major Danish rule: V2 word order.

Yes, but the basic sentence you have is the most neutral and natural.

Possible alternatives include:

• På bordet ved døren lægger jeg nøglen.
• Nøglen lægger jeg på bordet ved døren.

These versions change the emphasis. Danish allows this because the finite verb still stays in second position in a main clause.

Still, for a learner, the safest default is:

• Jeg lægger nøglen på bordet ved døren.

You would usually put ikke after the finite verb in a main clause:

• Jeg lægger ikke nøglen på bordet ved døren.

That means:

• I am not putting the key on the table by the door.
• or I do not put the key on the table by the door, depending on context

This placement of ikke is very common in Danish main clauses.

In modern spoken Danish, jeg is very often pronounced something like yai, yai/ya, or even more reduced depending on dialect and speed.

It is usually not pronounced the way an English speaker might expect from the spelling.

A practical learner note:

• spelling: jeg
• common everyday pronunciation: roughly yai

You will hear variation, but the written form is always jeg.

These are tricky for English speakers because Danish has vowels that English does not use in quite the same way.

• æ in lægger is somewhat like the vowel in English cat, but not exactly
• ø in nøglen is a rounded front vowel; English does not really have a direct equivalent

Very rough learner approximations:

• lægger ≈ LEH-ger with a more open front vowel
• nøglen ≈ something like NUH-len or NUR-len, but that is only an approximation

The best strategy is to listen repeatedly to native audio, especially for æ, ø, and reduced endings.

Because when the definite ending is added, Danish often changes the shape of the word a little.

The base noun is:

• nøgle = key

The definite form is:

• nøglen = the key

The final -e of the base form does not stay as a full extra syllable before the definite ending. This kind of change is very common in Danish noun forms and has to be learned word by word.

Similar patterns happen in many nouns, although not always in exactly the same way.

It can be either. Danish present tense often covers both meanings.

• Jeg lægger nøglen på bordet ved døren.

Depending on context, this could mean:

• I put the key on the table by the door as a habit
• I am putting the key on the table by the door right now

Danish often relies on context rather than changing the verb form the way English does with am putting.

Sometimes yes, but it is not exactly the same.

• lægger is the normal and most idiomatic verb for placing something in a lying position or putting something somewhere
• putter means put, but often with a sense like put into, stuff into, or place something, especially into a container or space

So:

• Jeg lægger nøglen på bordet sounds very natural
• Jeg putter nøglen på bordet is possible, but less neutral here

For this sentence, lægger is the best choice.