Learn Polish: Trzeba się uczyć.

Trzeba is an impersonal word, meaning it doesn't take a specific subject like I, you, or he. It simply means "one must," "it is necessary," or "people need to." Because there is no specific person doing the action, the verb that follows it (uczyć) stays in its dictionary form (the infinitive).

The dictionary form for "to study" is uczyć się. Why are the two words split up in this sentence?

In Polish, the word się is quite flexible, but it strongly prefers not to be the very last word in a sentence if it can be avoided. It also cannot be the very first word. To sound natural, Polish speakers tuck it into the middle, saying Trzeba się uczyć instead of Trzeba uczyć się.

I thought the verb uczyć meant "to teach"?

It does! However, when you add the word się (which generally means "oneself"), the meaning changes. While uczyć means "to teach" someone else, uczyć się literally means "to teach oneself"—which is the Polish way to say "to learn" or "to study".