Learn Hardcore Icelandic: Við undirbúum okkur fyrir viðtalið í kvöld.

fyrir + accusative: direction/goal, purpose, for (as here), sometimes before (time)
fyrir + dative: location ( in front of at rest), cause ( because of ), or responsibility/on behalf of (depending on context)

Við is the 1st‑person plural subject pronoun we. In modern Icelandic you normally keep the subject pronoun even though the verb ending already shows the person/number. Dropping við is uncommon outside of poetry, headlines, or very informal/context-heavy speech.

How is undirbúum formed, and what tense is it?

undirbúum is the verb undirbúa (to prepare) conjugated in present tense, 1st person plural.
Typical present endings for many verbs include -um for we.
So: (við) undirbúum = we prepare / we are preparing (depending on context).

Why is okkur there? What role does it play?

okkur means us and it’s used reflexively here: undirbúa sig = to prepare oneself.
With við (we), the reflexive object form is okkur (us/ourselves).
So the structure is literally: We prepare us → natural English: We prepare ourselves.

Is okkur accusative or dative here, and how can I tell?