Jeg lægger det gamle udkast i papirkurven, når jeg er færdig med rettelserne.

Because Danish, like English, distinguishes between putting something somewhere and being somewhere.

• at lægge = to lay, put
• at ligge = to lie, be located

In this sentence, the speaker is actively moving the draft into the wastebasket, so Danish uses lægger:

• Jeg lægger det gamle udkast i papirkurven = I put the old draft in the wastebasket

If the draft were already there, you would use ligger:

• Det gamle udkast ligger i papirkurven = The old draft is in the wastebasket

So a good shortcut is:

• lægge = action
• ligge = location/state

Danish often uses the present tense for a future action when the future event is understood from context.

So:

• Jeg lægger det gamle udkast i papirkurven, når jeg er færdig med rettelserne

literally looks like present tense, but it naturally means:

• I’ll put the old draft in the wastebasket when I’m finished with the corrections

This is very common in Danish, especially with time words like når.

You could say something with vil to make the future more explicit:

• Jeg vil lægge det gamle udkast i papirkurven ...

But the plain present often sounds more natural and matter-of-fact.

Here når means when or once.

In this sentence, it introduces an expected future moment:

• når jeg er færdig med rettelserne = when I am finished with the corrections

Useful comparison:

• når = when / whenever
  Used for repeated situations or expected future situations
• hvis = if
  Used for conditions
• da = when
  Usually for a specific past situation

Examples:

• Når jeg er færdig, går jeg hjem = When I’m done, I’m going home
• Hvis jeg bliver færdig, går jeg hjem = If I get done, I’ll go home
• Da jeg blev færdig, gik jeg hjem = When I finished, I went home

So in your sentence, når shows that finishing the corrections is expected, not just possible.

This is the normal way Danish forms a definite noun phrase with an adjective.

Break it down:

• et udkast = a draft
• gammel/gammelt = old
• det gamle udkast = the old draft

Why this form?

1. udkast is a neuter noun, so the definite article is det
2. In a definite phrase with an adjective, the adjective usually takes -e
   • gamle
3. The noun itself stays in its basic form after det + adjective
   • udkast, not udkastet

So:

• et gammelt udkast = an old draft
• det gamle udkast = the old draft

This is a very important pattern in Danish:

• det store hus = the big house
• den nye bog = the new book

Rettelserne is the definite plural form of rettelse.

The forms are:

• en rettelse = a correction / an edit
• rettelser = corrections / edits
• rettelserne = the corrections / the edits

So:

• med rettelserne = with the corrections / with the edits

The definite plural is used because these are specific corrections already understood in the situation.

Also, after the preposition med, Danish does not change the noun form the way some languages do. So the form stays rettelserne.

at være færdig med noget is a very common Danish expression meaning to be finished with something.

So:

• jeg er færdig med rettelserne = I am finished with the corrections
• jeg er færdig med arbejdet = I am finished with the work

You can also say just:

• jeg er færdig = I’m done

But if you want to say what you are done with, you use med:

• færdig med rettelserne
• færdig med lektierne
• færdig med rapporten

Because the draft is being put inside the wastebasket, not on top of it.

• i = in, inside
• på = on, on top of

So:

• i papirkurven = in the wastebasket
• på papirkurven = on the wastebasket

In this sentence, i is the natural choice because a paper basket is treated as a container.

Because Danish makes compound nouns very freely, much like German.

• papir = paper
• kurv = basket
• papirkurv = paper basket / wastebasket
• papirkurven = the paper basket / the wastebasket

This is completely normal in Danish: the parts are usually written together as one word.

Also, the last part of the compound determines the grammatical gender and ending. Since kurv is a common-gender noun (en kurv), the definite form becomes:

• papirkurven

After når, Danish uses normal subordinate clause word order:

• når jeg er færdig med rettelserne

That means the subject comes before the finite verb:

• jeg er

There is no inversion here.

In your full sentence, the main clause comes first:

• Jeg lægger det gamle udkast i papirkurven, når jeg er færdig med rettelserne.

If you move the når clause to the front, then the main clause must invert:

• Når jeg er færdig med rettelserne, lægger jeg det gamle udkast i papirkurven.

So the pattern is:

• subordinate clause first → verb before subject in the main clause
• subordinate clause after the main clause → main clause stays normal

This is a very important Danish word-order rule.