Hon lägger en ren handduk på sängen och ett varmt täcke i sovrummet.

This is a very common Swedish pair to confuse.

• lägger comes from lägga = to lay / put
• ligger comes from ligga = to lie / be lying

So:

• Hon lägger en handduk på sängen = she puts a towel on the bed
• Handduken ligger på sängen = the towel is lying on the bed

A good shortcut is:

• lägga = an action done to something
• ligga = the position something is in afterward

Swedish often uses different verbs for put, depending on the position of the object.

• lägga = put something so that it lies flat
• ställa = put something standing upright
• sätta = put something in a sitting position, or set/place in certain contexts

A towel and a blanket/duvet are things that normally end up lying, so lägger is the natural choice.

Because Swedish nouns have grammatical gender.

• handduk is an en-word (common gender)
  → en handduk
• täcke is an ett-word (neuter)
  → ett täcke

The article has to match the noun’s gender.

In this sentence:

• en ren handduk
• ett varmt täcke

You just have to learn each noun together with en or ett.

Swedish adjectives agree with the noun.

In the indefinite singular:

• with an en-word, the adjective usually has its basic form
  → en ren handduk
• with an ett-word, the adjective usually adds -t
  → ett varmt täcke

So:

• ren matches en handduk
• varmt matches ett täcke

A very useful pattern is:

• en
  • adjective base form + noun
• ett
  • adjective + -t
    • noun
• plural/definite often use -a

Because Swedish usually puts the definite article on the end of the noun.

• säng = bed

• sängen = the bed

• sovrum = bedroom
• sovrummet = the bedroom

So instead of a separate word like English the, Swedish often uses a suffix:

• common gender nouns often take -en or -n
• neuter nouns often take -et or -t

Because they mean different things.

• på sängen = on the bed, on top of it
• i sängen = in bed / in the bed

Here the towel is being placed on top of the bed, so på sängen is correct.

This is an important distinction in Swedish.

Because i means in / inside.

So:

• i sovrummet = in the bedroom
• på sängen = on the bed

The sentence uses two different prepositions because the relationships are different:

• the towel is placed on the bed
• the blanket/duvet is placed in the bedroom

In normal reading, it goes with the second item only.

So the sentence is understood as:

• she puts a clean towel on the bed
• and a warm blanket/duvet in the bedroom

In other words, the structure is roughly:

• [en ren handduk på sängen]
• och [ett varmt täcke i sovrummet]

If you wanted both things to go on the bed, you would normally say something like:

• Hon lägger en ren handduk och ett varmt täcke på sängen.

Because Swedish, like English, often leaves out a repeated verb when it is understood.

So this is perfectly normal:

• Hon lägger en ren handduk på sängen och ett varmt täcke i sovrummet.

It means the same as the fuller version:

• Hon lägger en ren handduk på sängen och lägger ett varmt täcke i sovrummet.

The second lägger is unnecessary because the first one already covers both coordinated parts.

Yes. This is a very normal main-clause pattern:

• Subject + verb + object + place

Here:

• Hon = subject
• lägger = verb
• en ren handduk = object
• på sängen = place
• och ett varmt täcke i sovrummet = coordinated second object + place

You can move things around for emphasis, but then Swedish still follows the V2 rule: the finite verb stays in second position.

For example:

• På sängen lägger hon en ren handduk ...

That is possible, but more marked than the original sentence.

Then Swedish usually uses double definiteness when there is an adjective.

So:

• den rena handduken = the clean towel
• det varma täcket = the warm blanket/duvet

Notice two things happen:

1. you add a separate definite word
   
   • den / det
2. the noun also gets its definite ending
   
   • handduken, täcket

And the adjective usually takes -a:

• rena
• varma

Not always.

Täcke often means something like:

• duvet
• quilt
• bedcover
• blanket used on a bed

If you mean a more general blanket or throw, Swedish often uses filt.

So in many contexts, täcke is better understood as a bed covering, not just any blanket.

Yes. That is the safest approach.

For this sentence, it is useful to learn them as complete units:

• en handduk
• en säng
• ett täcke
• ett sovrum

That helps with:

• choosing en or ett
• getting adjective endings right
• forming the definite correctly later

Learning the article together with the noun is one of the best habits in Swedish.