Dúkkan situr á gólfinu við hliðina á kubbunum.

Yes:

• Dúkkan = the doll
• situr = sits / is sitting
• á gólfinu = on the floor
• við hliðina á kubbunum = next to the blocks

A very literal version would be:

The doll sits on the floor by the side of the blocks.

Because dúkkan is the definite form, meaning the doll.

The basic noun is:

• dúkka = a doll

With the definite article added:

• dúkkan = the doll

In Icelandic, the is usually attached to the end of the noun instead of being a separate word as in English.

Also, dúkkan is in the nominative singular here because it is the subject of the sentence.

Because sitja is the infinitive, meaning to sit.

In the sentence, you need a conjugated verb:

• sitja = to sit
• situr = sits / is sitting

Since dúkkan is third person singular (the doll, she/it), the verb has to match that form, so Icelandic uses situr.

It can mean either, depending on context.

In Icelandic, the simple present often covers both:

• she sits
• she is sitting

In a scene description like this one, English often prefers is sitting, but Icelandic naturally just says situr.

If you really want to emphasize an ongoing action, Icelandic can also use er að sitja, but that is not necessary here.

Because á changes case depending on whether you mean location or movement.

Here, the doll is already sitting on the floor, so this is location, and Icelandic uses the dative:

• á gólfinu = on the floor

If there were movement onto the floor, Icelandic would typically use the accusative:

• á gólfið = onto the floor

So the contrast is roughly:

• location → dative
• movement toward a place → accusative

The base noun is:

• gólf = floor

Here it appears as gólfinu, which is the dative singular definite form.

So:

• gólf = a floor
• gólfinu = the floor in the case required by the preposition

This is another example of Icelandic attaching the to the noun itself.

Við hliðina á is a very common expression meaning:

• next to
• beside

It is best learned as a whole chunk.

Literally, it is something like:

• by the side of

So in this sentence:

• við hliðina á kubbunum = next to the blocks

Even though it looks longer than the English equivalent, it functions as one ordinary location expression.

Because the Icelandic expression is built that way.

It is not just a single word for next to. Instead, Icelandic uses a phrase that is roughly:

• við
  • the side
    • of

So:

• við hliðina á = next to / beside

This is very normal in Icelandic. The most useful approach is to memorize við hliðina á as one fixed expression rather than trying to translate each little part separately every time.

Because kubbunum is the form of kubbur that fits the phrase.

The base noun is:

• kubbur = block / toy block / cube-shaped block

In the sentence, it is:

• plural = more than one block
• definite = the blocks
• in the dative, because á in við hliðina á requires that case

So:

• kubbar = blocks
• kubbunum = the blocks in the required case

Because the Icelandic definite article changes depending on:

• gender
• number
• case

So all of these include the idea of the, but in different grammatical forms:

• Dúkkan = the doll
• gólfinu = the floor
• kubbunum = the blocks

English uses the separate word the for all of them, but Icelandic builds that meaning into the noun ending.

This sentence has a very straightforward word order:

• Dúkkan = subject
• situr = verb
• then the location phrases

So it looks quite similar to English:

• The doll sits/is sitting on the floor next to the blocks.

That said, Icelandic is a verb-second language in main clauses, so if you move another element to the front, the verb still normally stays in second position. For example, Icelandic can also say things like:

• Á gólfinu situr dúkkan ...

That sounds more marked, but it shows the same grammar.