Learn Croatian: Pokazali su učitelju put. - They showed the teacher the way.

It is in the dative case. In this sentence, the teacher is the indirect object—the person receiving the action of being shown something. For masculine nouns like učitelj, we add the ending -u to make it dative singular.

Where is the word for 'they' in this sentence?

Croatian frequently drops subject pronouns like oni (they) because the verb already tells you who is doing the action. Here, the plural helper verb su combined with the plural ending on pokazali makes it clear that 'they' showed the way.

The word put (way) is the direct object. Why didn't its ending change for the accusative case?

It actually is in the accusative case! Put is a masculine noun that refers to a non-living thing (inanimate). For masculine inanimate nouns, the accusative form is exactly the same as the dictionary (nominative) form.

Why do we need the word su here?

To talk about the past in Croatian, you almost always need two parts: an action word ending in -l, -la, -li, etc., and a helper verb. The helper verb here is su (a form of the verb 'to be'). Without su, the past tense would be incomplete.