Learn Polish: Ten hotel jest gorszy.

Just like in English (bad -> worse), the Polish word for "bad" (zły) has an irregular comparative form. You don't add a standard comparative ending to its base; instead, the root of the word completely changes to gorszy.

Why does gorszy end in -y in this sentence?

Because it is an adjective describing hotel, which is a masculine noun. If you were talking about a feminine noun like a restaurant (restauracja), it would be gorsza, and for a neuter noun like a car (auto), it would be gorsze.

How would I change this sentence to say "This hotel is the worst"?

To make the superlative (meaning "the most" or "the worst"), you simply add the prefix naj- to the comparative form. So, gorszy becomes najgorszy, and the sentence would be Ten hotel jest najgorszy.

Could I use gorszy if I wanted to say someone sleeps "worse" in this hotel?

No, gorszy is an adjective, meaning it only describes nouns (like the hotel itself). To describe an action like sleeping, you need the adverb form, which is gorzej. For example: Śpię tu gorzej (I sleep worse here).