Learn Hardcore Russian: Учитель объясняет инфинитив студентам. - The teacher explains the infinitive to the students.

In Russian, the verb объяснять (to explain) is ditransitive: it takes a direct object (what is being explained) in the accusative and an indirect object (to whom it is explained) in the dative. Here студентам (students) answers the question кому? (to whom?), so it must be in the dative plural.

Why is инфинитив in the accusative case?

Инфинитив (infinitive) is the direct object of объясняет, answering что? (what?). Because it’s an inanimate masculine noun in the singular, its nominative and accusative forms coincide as инфинитив.

What objects does the verb объяснять require, and how do I recognize them?

Объяснять requires two objects:
1) A direct object in the accusative (что? – инфинитив)
2) An indirect object in the dative (кому? – студентам)
You spot them by asking the questions что? for the thing explained and кому? for the person receiving the explanation.

How would I form студентам from студент?