Learn Croatian: Učitelj vas želi pozdraviti. - The teacher wants to greet you.

vas is a clitic, which means it's a short, unstressed pronoun. In Croatian, clitics almost always have to take the second position in a sentence. Because the subject Učitelj takes the first spot, vas must slide in right after it, pushing the verb želi to the third spot.

Does vas mean multiple people here, or just one person?

It could be either! vas is the accusative object form of vi. This can mean plural "you" (a group of people) or the formal, polite "you" (a single person the teacher is showing respect to).

If I wanted to say "The teacher wants to greet us", how would the sentence change?

You would simply swap out the clitic. The accusative clitic for "us" is nas, so the sentence would be: Učitelj nas želi pozdraviti.

Why isn't there a word for "to" between želi and pozdraviti?

In Croatian, the "to" is already built into the dictionary form of the verb, called the infinitive. pozdraviti entirely means "to greet". When you connect a main verb like želi (wants) with an action, the second verb just stays in this infinitive form.