Jag packar upp böckerna först och ställer dem på en hylla.

Because packa upp is a particle verb in Swedish, similar to English unpack or pack up.

In a main clause, the finite verb comes early, and the particle usually comes later:

• Jag packar upp böckerna = I unpack the books

So:

• packar = the present-tense verb
• upp = the particle

You will often see this pattern with Swedish particle verbs:

• skriva upp = write down
• städa upp = tidy up
• äta upp = eat up

In some other forms, the two parts can appear together:

• att packa upp = to unpack
• har packat upp = have unpacked

Packa upp usually means to unpack.

It is the opposite of packa ner, which means to pack down / pack away.

Examples:

• Jag packar upp väskan. = I unpack the bag.
• Vi packar upp efter flytten. = We unpack after the move.

So in your sentence, Jag packar upp böckerna först means that the speaker is taking the books out and getting them ready before putting them somewhere.

Böckerna is the definite plural form, meaning the books.

• en bok = a book
• boken = the book
• böcker = books
• böckerna = the books

So:

• Jag packar upp böcker. = I unpack books
• Jag packar upp böckerna. = I unpack the books

Swedish often attaches the definite article to the end of the noun instead of using a separate word like the.

This is an irregular plural pattern:

• en bok = a book
• böcker = books
• böckerna = the books

What changes:

1. bok becomes böck-
2. plural ending -er is added → böcker
3. definite plural ending -na is added → böckerna

This vowel change (o → ö) is common in some Swedish nouns.

Because dem is the object form of they.

• de = they
• dem = them

In your sentence, böckerna is the thing being acted on in the second part:

• ställer dem på en hylla = put them on a shelf

So dem is correct because it works like English them.

A quick comparison:

• De står på hyllan. = They are standing on the shelf.
• Jag ställer dem på hyllan. = I put them on the shelf.

In everyday speech, de and dem are both usually pronounced like dom, but in writing the distinction is still standard.

Because in Swedish, just like in English, you can often leave out the subject in the second part of a coordinated sentence when it is the same subject.

So this is natural:

• Jag packar upp böckerna först och ställer dem på en hylla.

This means:

• I unpack the books first and put them on a shelf.

You could say:

• Jag packar upp böckerna först och jag ställer dem på en hylla.

But that sounds heavier and less natural unless you want extra emphasis.

So omitting the second jag is normal and idiomatic.

Först means first, and here it tells you when the unpacking happens in relation to the next action.

• Jag packar upp böckerna först och ställer dem på en hylla.

The idea is:

1. first, I unpack the books
2. then, I put them on a shelf

Placing först after böckerna is very natural in Swedish.

You may also see other adverbs in similar positions:

• Jag läser boken först.
• Jag tvättar händerna först.

Swedish word order with adverbs can vary a little depending on emphasis, but this placement is completely normal.

Swedish often chooses different verbs depending on the position of the object.

• ställa = put something so that it stands upright
• lägga = lay something down
• sätta = set/seat something, often into a sitting position or certain placement contexts

Books on a shelf are commonly thought of as standing upright, so ställa is the natural choice:

• ställa böcker på en hylla = put books on a shelf

Compare:

• Jag lägger boken på bordet. = I lay the book on the table.
• Jag ställer flaskan på bordet. = I put the bottle on the table.
• Jag sätter barnet på stolen. = I seat the child on the chair.

This is one of those places where Swedish is a bit more specific than English put.

Because på is the normal preposition for something placed on a shelf.

A shelf is treated as a surface or support:

• på en hylla = on a shelf

So:

• Jag ställer dem på en hylla. = I put them on a shelf.

By contrast, i means in, and would be used for something inside an enclosed space:

• i en låda = in a box
• i ett skåp = in a cabinet

Even though a shelf may be part of a bookcase, Swedish still normally says på en hylla for the shelf itself.

En hylla means a shelf, while hyllan means the shelf.

The sentence uses the indefinite form because it does not specify exactly which shelf:

• på en hylla = on a shelf

If the speaker meant a particular known shelf, you could say:

• på hyllan = on the shelf

So the choice depends on whether the shelf is specific or not.

Both are present tense.

• packar = unpack / am unpacking
• ställer = put / am putting

In Swedish, the present tense often covers both simple present and present continuous ideas from English, depending on context.

So:

• Jag packar upp böckerna can mean
  • I unpack the books
  • I am unpacking the books

Likewise:

• ställer dem på en hylla can mean
  • put them on a shelf
  • am putting them on a shelf

The exact English translation depends on context.

Because Swedish usually expresses definiteness by adding an ending to the noun.

So instead of saying a separate word like the books, Swedish says:

• böckerna

This ending -na carries the meaning of the in the plural.

A few examples:

• boken = the book
• bilarna = the cars
• husen = the houses

So böckerna already includes the meaning the books.