Ég set eina teskeið af sykri í teið.

The dictionary form is setja, meaning to put / to place.

Here, set is the present tense, first person singular, because the subject is ég = I.

• ég set = I put / I am putting
• past tense: ég setti = I put
• infinitive: að setja = to put

So this sentence is built around the present-tense verb form set.

Because Icelandic normally writes compound nouns as a single word.

teskeið is made from:

• te = tea
• skeið = spoon

So literally it is tea-spoon. Icelandic is very consistent about this kind of compounding, often more consistent than English.

Because teskeið is the direct object of the verb set, so it is in the accusative case.

The word ein (one) has to agree with the noun in:

• gender
• number
• case

teskeið is feminine singular, so:

• nominative: ein teskeið
• accusative: eina teskeið

In this sentence, the spoonful is what is being put into the tea, so accusative is needed: eina teskeið.

Also notice that the noun teskeið itself does not visibly change here; the case difference shows up in ein/eina.

Basically one, but in translation it can overlap with English a/an because Icelandic has no separate indefinite article.

So:

• ein / eina / eitt = one
• but depending on context, English may translate it as a/an

In this sentence, eina teskeið most naturally means one teaspoon specifically. It emphasizes the quantity.

Because Icelandic often uses af after a measure word to mean of:

• teskeið af sykri = teaspoon of sugar
• glas af vatni = glass of water

The preposition af takes the dative case, so sykur becomes sykri.

So:

• nominative: sykur
• dative after af: sykri

That is why it is af sykri, not af sykur.

Because í can take either the accusative or the dative, depending on the meaning.

• accusative after í = movement/direction, often into
• dative after í = location, often in

Here, you are putting something into the tea, so Icelandic uses the accusative:

• í teið = into the tea

If you were only describing where something is, you would use the dative:

• sykurinn er í teinu = the sugar is in the tea

So the contrast is:

• setja ... í teið = put ... into the tea
• vera í teinu = be in the tea

It is the definite article attached to the noun.

Icelandic usually puts the at the end of the word instead of using a separate word before it.

So:

• te = tea
• teið = the tea

This is very common in Icelandic:

• hús = house
• húsið = the house

In this sentence, teið refers to a specific tea, for example the tea in the cup being discussed.

Yes. This is a very normal, neutral Icelandic word order:

• Ég = subject
• set = verb
• eina teskeið af sykri = direct object
• í teið = prepositional phrase

So the basic pattern is:

Subject + Verb + Object + Prepositional phrase

Icelandic can move elements around for emphasis, but the version you have is the straightforward default.

Usually no. Standard Icelandic normally keeps the subject pronoun, so ég is expected here.

Unlike some languages, Icelandic is not usually a pronoun-dropping language in ordinary statements.

So:

• Ég set ... = normal
• leaving out ég would usually sound incomplete in a plain statement

If this were an instruction to someone, you would use an imperative instead:

• Settu eina teskeið af sykri í teið. = Put one teaspoon of sugar in the tea.

So in the sentence you gave, ég is there because it is a normal finite statement: I put / I am putting ...