På lördag måste vi damma bokhyllan och vika kläderna.

It means on Saturday, often with the sense of this coming Saturday if the context is about the future.

Swedish commonly uses på with days of the week in this kind of sentence:

• på måndag = on Monday
• på fredag = on Friday
• på lördag = on Saturday

A useful contrast:

• på lördag = this coming/on Saturday
• i lördags = last Saturday
• på lördagar = on Saturdays, in general

This is because Swedish follows the V2 rule: the finite verb usually comes in the second position in a main clause.

Here, På lördag is placed first, so the finite verb måste has to come next:

• På lördag måste vi damma bokhyllan ...

If the subject comes first instead, then the order is:

• Vi måste damma bokhyllan på lördag.

Both are correct. The first version puts more focus on the time.

No. In modern Swedish, verbs do not change for person the way they do in English.

So you get:

• jag måste = I must / I have to
• du måste = you must
• vi måste = we must
• de måste = they must

The form måste stays the same.

They are in the infinitive form, because they come after the modal verb måste.

After måste, Swedish uses the basic verb form:

• måste damma
• måste vika
• måste gå
• måste läsa

So in this sentence:

• måste vi damma bokhyllan och vika kläderna

both damma and vika are infinitives controlled by måste.

Because after modal verbs such as måste, kan, vill, ska, and får, Swedish normally uses the bare infinitive — that is, the infinitive without att.

So:

• vi måste damma
• hon kan komma
• jag vill läsa

Not:

• vi måste att damma

That would be incorrect.

Because Swedish usually writes compound nouns as a single word.

bokhylla is made up of:

• bok = book
• hylla = shelf

So:

• bokhylla = bookshelf / bookcase

Then the definite ending is added to the whole compound:

• bokhyllan = the bookshelf / the bookcase

This is very common in Swedish:

• kaffekopp = coffee cup
• sommarhus = summer house
• sjukhus = hospital

In Swedish, the definite article is often attached to the noun as a suffix.

So:

• en bokhylla = a bookshelf
• bokhyllan = the bookshelf

Because bokhylla is an en-word, the definite singular ending is -n here:

• bokhylla → bokhyllan

English uses a separate word, the, but Swedish often builds that meaning into the noun itself.

kläder means clothes, while kläderna means the clothes.

So:

• vika kläder = fold clothes
• vika kläderna = fold the clothes

In Swedish, the definite form is very common when the speaker means a specific set of clothes that both people understand from context — for example, the laundry at home.

The ending -na is the plural definite ending here:

• kläder = clothes
• kläderna = the clothes

och means and and links the two actions:

• damma bokhyllan
• vika kläderna

Both verbs depend on måste, so Swedish does not need to repeat it:

• På lördag måste vi damma bokhyllan och vika kläderna.

This is the same idea as in English:

• On Saturday we have to dust the bookshelf and fold the clothes.

You do not need to repeat we have to before the second verb.

Yes. damma can be used transitively, so damma bokhyllan means dust the bookshelf.

That is a normal pattern:

• damma bordet = dust the table
• damma hyllorna = dust the shelves

You may also sometimes hear forms like damma av, which can emphasize dusting off something, but in a simple household-chore sentence, damma bokhyllan is completely natural.

Yes. A very natural alternative is:

• Vi måste damma bokhyllan och vika kläderna på lördag.

That version starts with the subject vi instead of the time expression. The meaning is basically the same, but the emphasis changes slightly:

• På lördag måste vi ... = highlights when
• Vi måste ... på lördag = more neutral, or slightly more focused on what we have to do

Both are correct Swedish.