Learn Icelandic: Kennarinn mun setja upp vinnuborðið. - The teacher will set up the workbench.

Because vinnuborðið is a full noun. In Icelandic phrasal verbs, the particle (like upp) comes before a full noun object. If the object were a pronoun instead, the order would flip and the pronoun would squeeze in the middle: Kennarinn mun setja það upp (The teacher will set it up).

Why is the verb setja in the infinitive form here?

It follows the auxiliary verb mun (will). Just like in English, when you use a helper verb to show the future tense, the main action verb that comes after it stays in its basic, un-conjugated dictionary form.

What case is the word vinnuborðið in?

It is in the accusative case because it is the direct object receiving the action. The verb setja triggers the accusative case for the thing being placed or set up. Since vinnuborð is a neuter word, its accusative form looks exactly the same as its nominative form.

Does setja upp work for everything that translates to 'set up' in English?

It is very similar, but it mostly applies to physical assembly, installation, or putting something on display (like erecting a tent or staging a play). If you mean setting up a meeting or an abstract concept, you would usually use different verbs like skipuleggja (organize) or stofna (establish, found).