Ég er að skera tómata smátt í eldhúsinu.

Ég er að + infinitive is a very common way to express an action in progress, similar to English I am cutting.
Ég sker is the simple present and often reads more like a habitual/general statement (I cut / I do cut tomatoes) unless context makes it “right now”.

Here að is an infinitive marker (often comparable to English to), introducing the infinitive skera. In the construction vera að + infinitive, it helps form the “ongoing action” meaning.

Because the finite (conjugated) verb in this sentence is er (from vera, to be). After er að, Icelandic uses the infinitive: (ég) er að skera.

tómatar is nominative plural (typically the subject form).
Here tómata is accusative plural, because skera (to cut) takes a direct object, and direct objects are very often in the accusative in Icelandic.

Common plural forms are:

• Nominative: tómatar
• Accusative: tómata (used here)
• Dative: tómötum
• Genitive: tómata

So tómata can be either accusative plural (as here) or genitive plural (in other contexts).

eldhúsinu is dative singular with the definite article (“the kitchen”).
The ending -inu = eldhús-i-nu:

• eldhús (stem)
• -i (dative singular ending)
• -nu (the definite article in that form)

So í eldhúsinu = in the kitchen (specific/known kitchen).

With location (“where”), í takes the dative: í eldhúsinu = “in the kitchen.”
With motion/destination (“to/into where”), í usually takes the accusative:

• Ég fer í eldhúsið = “I go into the kitchen.”

Here smátt functions as an adverb meaning “finely / into small pieces.” It’s historically the neuter form of an adjective and is commonly used adverbially in Icelandic.

This placement is common: skera tómata smátt = “cut tomatoes finely.”
You can also see alternatives depending on emphasis, but object + adverb is very natural here. Putting smátt earlier can sound more marked or stylistic.