Jeg lægger nålen i skuffen.

Because Danish usually marks the by adding it to the end of the noun instead of putting a separate article in front.

• en nål = a needle
• nålen = the needle
• en skuffe = a drawer
• skuffen = the drawer

So in this sentence, both nouns are definite: it is a specific needle and a specific drawer.

The dictionary forms are:

• nål = needle
• skuffe = drawer

With the common-gender article, they are:

• en nål
• en skuffe

Then the definite singular forms are:

• nålen
• skuffen

Both are en-words in Danish, which is why the definite ending is -en.

Lægger is the present tense of the verb at lægge.

So:

• at lægge = to lay / to put
• lægger = lay / lays / am putting / is putting, depending on context

A very useful pattern is that Danish present-tense verbs usually end in -r.

Examples:

• jeg lægger
• du lægger
• han lægger
• vi lægger

The form stays the same for all persons.

This is one of the most important Danish verb pairs to learn.

• lægge = to lay/put something somewhere
  
  • it usually takes a direct object
• ligge = to lie/be lying somewhere
  
  • it describes position, not the act of placing

So:

• Jeg lægger nålen i skuffen. = I am placing the needle in the drawer.
• Nålen ligger i skuffen. = The needle is lying in the drawer.

A simple way to remember it:

• lægge = movement / placement
• ligge = location / result

No. Danish verbs do not change for person or number in the present tense.

So you get:

• jeg lægger
• du lægger
• hun lægger
• vi lægger
• de lægger

That makes Danish verb conjugation much simpler than English in this area.

Because Danish usually uses the simple present where English often uses either simple present or present continuous.

So Jeg lægger nålen i skuffen can match English:

• I put the needle in the drawer
• I am putting the needle in the drawer

The exact English translation depends on context.

If Danish wants to stress that something is in progress, it can use a construction like:

• Jeg er ved at lægge nålen i skuffen.

That is closer to I am in the process of putting the needle in the drawer.

Here i corresponds to English in, but with a verb like lægge, the whole sentence naturally gives the idea of putting something into something.

Danish often lets the verb show the movement, so i is enough.

• Nålen ligger i skuffen. = The needle is in the drawer.
• Jeg lægger nålen i skuffen. = I put the needle in the drawer.

If you want to make the movement even more explicit, Danish can also say:

• ind i

For example:

• Jeg lægger nålen ind i skuffen.

But in many everyday sentences, just i is perfectly natural.

Yes, often you could say:

• Jeg putter nålen i skuffen.

That also means I put the needle in the drawer.

The difference is roughly:

• lægger suggests laying/placing something down
• putter is more general and often a bit more colloquial, like put

For a small object like a needle, both can work, but lægger is a very natural choice.

This is the normal Danish main-clause order:

• subject
  • finite verb
    • object
      • prepositional phrase

So:

• Jeg = subject
• lægger = finite verb
• nålen = direct object
• i skuffen = prepositional phrase

Danish main clauses follow the V2 rule, which means the finite verb is usually in the second position.

For example, if you start with another element, the verb still stays second:

• Nu lægger jeg nålen i skuffen.
• I skuffen lægger jeg nålen.

That second example is possible, but more marked or stylistically special than the basic order.

You would use the indefinite forms when you mean a needle or a drawer, not a specific one already known from the context.

Compare:

• Jeg lægger nålen i skuffen.
  = a specific needle, a specific drawer

• Jeg lægger en nål i en skuffe.
  = some needle in some drawer

In real speech, the definite forms are very common when both speaker and listener know which objects are being talked about.

Yes, very often Danish chooses placement verbs based on the object's position.

Common pairs include:

• lægge / ligge for things that are laid down
• stille / stå for things that stand upright
• sætte / sidde for things that are set in a sitting position or attached in a certain way

So for a needle, lægge makes good sense because you normally place it down flat.

That said, real usage is not always perfectly mechanical, and native speakers sometimes choose the more general verb putte instead. Still, learning lægge vs. ligge early is very helpful.