Jeg lægger dine bøger på bordet.

Because Danish makes the same distinction as English lay vs lie:

• lægge = to lay / put / place something somewhere
• ligge = to lie / be lying somewhere

In this sentence, the subject is actively moving the books to the table, so Danish uses lægger:

• Jeg lægger dine bøger på bordet. = I put/am putting your books on the table.

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

• Dine bøger ligger på bordet. = Your books are lying on the table.

So a useful shortcut is:

• lægge = movement, caused by someone
• ligge = position, no movement

Lægger is the present tense of lægge.

Danish present tense is often formed by adding -r to the infinitive:

• at lægge = to put
• lægger = put / puts / am putting / is putting

Danish does not usually use a separate form like English am putting. The simple present can cover both:

• I put your books on the table
• I am putting your books on the table

Context tells you which is meant.

Because bøger is plural, and the possessive adjective must match that.

The forms are:

• din = your, for a singular common-gender noun
• dit = your, for a singular neuter noun
• dine = your, for plural nouns

Examples:

• din bog = your book
• dit bord = your table
• dine bøger = your books

So since bøger means books, the correct form is dine.

Because bog has an irregular plural.

• en bog = a book
• bøger = books

This is common in Danish: some nouns do not just add a simple ending; they may also change the vowel.

So you should learn this word as a set of forms:

• en bog
• bogen
• bøger
• bøgerne

These mean:

• a book
• the book
• books
• the books

In Danish, the definite article is usually added to the end of the noun, instead of coming before it.

So:

• et bord = a table
• bordet = the table

This is one of the most important differences from English.

Compare:

• English: the table
• Danish: bord-et

The ending depends on the gender and number of the noun. Here bord is a neuter noun, so the definite singular ending is -et.

Danish nouns have two grammatical genders:

• common gender (takes en)
• neuter (takes et)

Bord is a neuter noun, so:

• et bord = a table
• bordet = the table

Unfortunately, you usually have to learn the gender together with the noun. So it is best to memorize nouns with their article:

• en bog
• et bord

That makes it easier to form correct phrases later.

På usually means on.

So:

• på bordet = on the table

In this sentence, it shows where the books are being placed.

A useful thing to know is that Danish often uses the same preposition both for location and for placement:

• Bøgerne ligger på bordet. = The books are on the table.
• Jeg lægger bøgerne på bordet. = I put the books on the table.

English sometimes distinguishes on vs onto, but Danish often just uses på.

Most directly, it is present tense, so it usually means:

• I put
• I am putting

Depending on context, Danish present tense can sometimes also refer to the near future:

• Jeg lægger dine bøger på bordet senere. = I’ll put your books on the table later.

So the exact time meaning depends on the situation, not just the verb form.

This sentence has the normal main-clause word order:

• Jeg = subject
• lægger = verb
• dine bøger = object
• på bordet = adverbial/prepositional phrase

So the pattern is basically:

Subject + Verb + Object + Place

That is the most neutral way to say it.

Danish is a V2 language, which means the finite verb normally comes in the second position in main clauses. If you move another element to the front, the verb still stays second:

• På bordet lægger jeg dine bøger.
• Dine bøger lægger jeg på bordet.

Those are possible, but less neutral than the original sentence.

Yes, but it means something slightly different.

• dine bøger = your books
• bøgerne = the books

So:

• Jeg lægger dine bøger på bordet. = I put your books on the table.
• Jeg lægger bøgerne på bordet. = I put the books on the table.

If the meaning is specifically your books, then dine bøger is the right phrase.

There actually is a plural marker in dine: the form dine itself is the plural possessive form.

So both words show plural information:

• dine = your + plural
• bøger = books + plural

This kind of agreement is normal in Danish noun phrases.

Compare:

• din bog = your book
• dine bøger = your books

Pronunciation can vary a bit by region, but a rough guide is:

• jeg ≈ yai / yigh
• lægger ≈ LEH-guh
• bøger ≈ BUR-guh or BER-guh with a rounded vowel that English does not really have

A few important points:

• j in Danish is like English y
• g is often softer than English learners expect
• ø is a front rounded vowel, which may be unfamiliar

If you want a learner-friendly approximation of the whole sentence, something like this can help at first:

• yai LEH-guh DEE-nuh BUR-guh poh BOR-theth

But that is only approximate. Real Danish pronunciation is usually softer and more reduced than spelling suggests.

Usually yes. Lægge is the normal verb for physically putting something down in a place.

It suggests deliberate placement:

• placing books on a table
• setting something down
• laying something somewhere

For books, this is the most natural verb.

If you used a different verb, the meaning might shift. For example:

• sætter is more often used for setting upright objects or seated beings
• stiller often suggests placing something standing upright
• lægger fits things like books, clothes, papers, and anything laid down flat

So lægger is a very natural choice here.

Yes, and that is normal in Danish.

The distinction between:

• on the table (location)
• onto the table (direction)

is often not shown by changing the preposition. Danish simply uses på in both situations.

The verb tells you what is happening:

• ligger på bordet = is on the table
• lægger på bordet = puts on the table

So the combination of the verb and prepositional phrase gives the full meaning.