Kan du lägga kritan på bordet?

Because kan is a modal verb, and after a modal verb Swedish normally uses the infinitive form of the main verb.

• kan = can
• lägga = to put / to place

So:

• Kan du lägga ...? = Can you put ...?

You would use lägger if it were the main finite verb in the sentence, for example:

• Du lägger kritan på bordet. = You put / are putting the crayon on the table.

Kritan is the definite singular form of krita.

• en krita = a crayon / a piece of chalk
• kritan = the crayon / the piece of chalk

In Swedish, the definite article is often added as an ending:

• en bok → boken
• en stol → stolen
• en krita → kritan

So kritan means that a specific crayon is meant.

For the same reason: bordet is the definite singular form of bord.

• ett bord = a table
• bordet = the table

This word is an ett-word, so the definite ending is -et:

• ett hus → huset
• ett äpple → äpplet
• ett bord → bordet

So på bordet means on the table, not just on a table.

Swedish nouns belong to two grammatical genders/common article types:

• en-words
• ett-words

In this sentence:

• krita is an en-word → en krita, kritan
• bord is an ett-word → ett bord, bordet

Unfortunately, there is no fully reliable rule that lets you guess every noun’s type, so learners usually need to memorize it with the noun.

A very good habit is to learn nouns like this:

• en krita
• ett bord

not just krita and bord

Here på means on.

• på bordet = on the table

Swedish often uses på when something is resting on a surface. That matches English quite closely in this case.

Compare:

• på bordet = on the table
• i lådan = in the drawer / box
• under bordet = under the table

So på is the natural preposition if the crayon is being placed on top of the table.

Grammatically, it looks like Can you ...?, so yes, it literally asks about ability. But in normal usage, it is very often a request, just like in English.

So:

• Kan du lägga kritan på bordet? usually means
  Can you put the crayon on the table?
  = a request

It does not usually sound strange or overly literal. Swedish commonly uses Kan du ...? for polite everyday requests.

Yes, it is a normal and polite everyday request.

• Kan du lägga kritan på bordet? = neutral, natural
• adding snälla can make it softer:
  • Kan du lägga kritan på bordet, snälla? = Can you put the crayon on the table, please?

You could also hear:

• Kan du vara snäll och lägga kritan på bordet?
  = Could you please put the crayon on the table?

But the original sentence is already perfectly acceptable and polite in ordinary conversation.

Because this is a question, and in Swedish yes/no questions the finite verb usually comes first.

The finite verb here is kan, so the order is:

• Kan
  • du
    • lägga kritan på bordet?

Compare:

• Statement: Du kan lägga kritan på bordet. = You can put the crayon on the table.
• Question: Kan du lägga kritan på bordet? = Can you put the crayon on the table?

So the verb-first structure is a basic question pattern in Swedish.

You would usually put inte after the subject in this kind of sentence:

• Kan du inte lägga kritan på bordet?

This can mean:

• Can’t you put the crayon on the table?
• or sometimes a softer, persuasive request depending on tone

Word order:

• Kan = finite verb
• du = subject
• inte = not
• lägga = infinitive

So the pattern is:

• Kan du inte + infinitive ... ?

Du means you, and in modern Swedish it is used both in informal and most formal everyday situations.

Unlike some languages, Swedish does not normally use a special formal you in ordinary speech. So du is the standard word whether you are talking to a friend, a stranger, a colleague, or a teacher.

That means:

• Kan du lägga kritan på bordet? is completely normal

A careful approximate pronunciation is:

Kan du lägga kritan på bordet?
≈ kahn du LEG-ga KREE-tan paw BOOR-det

A few useful notes:

• kan has a broad a
• lägga has stress on the first syllable: LÄG-ga
• kritan has stress on the first syllable: KRI-tan
• bordet has stress on bor-

Also, in natural speech, du is often pronounced quite lightly.

Usually no, not for a crayon.

Swedish often distinguishes between different ways of placing things:

• lägga = lay/put something that ends up lying
• ställa = stand/put something that ends up standing
• sätta = set/put something into a sitting position, or place certain smaller objects in some contexts

A crayon normally lies on a table, so lägga is the natural choice.

So:

• lägga kritan på bordet = natural
• ställa kritan på bordet = only if you specifically mean standing it upright, which is not the normal default