Ég set teskeiðina á borðið við hliðina á bollanum.

Setja is the infinitive, meaning to put / to place. In the sentence, you need the finite verb form that matches ég (I), so it becomes set.

• að setja = to put
• ég set = I put / I am putting

So Ég set ... is correct, while Ég setja ... would be like saying I to put ... in English.

Because it means the teaspoon and it is the direct object of the verb, so it appears in the accusative singular definite form.

Breakdown:

• teskeið = teaspoon
• teskeiðin = the teaspoon (nominative)
• teskeiðina = the teaspoon (accusative)

Icelandic usually puts the definite article on the end of the noun instead of using a separate word like English the.

This is a very common Icelandic pattern: many prepositions change case depending on whether there is movement or location.

With á:

• accusative = motion onto something
• dative = being on something

Here, the spoon is being placed onto the table, so Icelandic uses the accusative:

• á borðið = onto the table

If you were just describing where it already is, you would normally use dative:

• Teskeiðin er á borðinu. = The teaspoon is on the table.

Because borð is a neuter noun, and for many neuter nouns the nominative and accusative singular look the same.

So:

• borðið can be nominative definite singular
• borðið can also be accusative definite singular

You know it is accusative here because of the preposition pattern á + accusative when there is movement onto something.

It means next to or beside.

It is best learned as a whole expression:

• við hliðina á = next to / beside

Literally, it is something like by the side of, but you should not try to translate each word too mechanically every time. Icelandic very often uses fixed phrases like this, and this is one of them.

Because the sentence contains two different structures:

1. á borðið = onto the table
2. við hliðina á bollanum = next to the cup

So the two á's do different jobs:

• the first á is the normal preposition meaning on/onto
• the second á is part of the fixed expression við hliðina á

They just happen to both be spelled á.

Because after við hliðina á, the noun that follows goes in the dative.

The base noun is:

• bolli = cup

Its definite dative singular form is:

• bollanum = the cup (dative)

So:

• við hliðina á bollanum = next to the cup

This is a good example of why it helps to learn prepositions and prepositional phrases together with the case they require.

In this expression, Icelandic normally uses the definite form:

• við hliðina á = next to / beside

So even though English just says next to, Icelandic uses a phrase that is more like at the side of. That is why you see the ending that corresponds to the side.

For learners, the safest approach is to memorize við hliðina á as one chunk.

Yes, in this sentence it is quite similar:

• Ég = subject
• set = verb
• teskeiðina = object
• á borðið við hliðina á bollanum = place/direction phrase

So the structure is roughly:

I + put + the teaspoon + onto the table next to the cup

However, Icelandic word order is not always identical to English. In main clauses, Icelandic follows a verb-second pattern, so if another element comes first, the verb still normally stays in second position.

You would remove the suffixed definite article, but the case endings would still matter.

Relevant forms here would be:

• teskeið = a teaspoon / teaspoon
• borð = a table / table
• bolla = a cup / cup in the form needed after við hliðina á

So the fully indefinite version would be:

Ég set teskeið á borð við hliðina á bolla.

That said, bare nouns in Icelandic do not always line up perfectly with English a/an, so the most natural choice can depend on context.