Learn Russian: Они изучают новый язык.

The dictionary form is изучать (to study), which is a standard first conjugation verb. For the pronoun они (they), we drop the -ть ending and add -ют, making it изучают.

Why use изучают here instead of another word for studying?

We use изучать when talking about studying a specific subject in depth, like a language, a science, or history. It always takes a direct object, which is exactly what we have here with новый язык.

Since новый язык is the direct object, why didn't its endings change?

Because язык (language) is a masculine, inanimate noun. In the accusative case (which marks the direct object), masculine words for non-living things keep their original dictionary endings. The adjective новый (new) also copies this rule.

Does the word язык mean anything else besides language?

Yes, язык can mean both a spoken language and the physical tongue in your mouth. You can easily tell which one is meant from the context of the sentence.