Learn Russian: Официант берёт чаевые.

Чаевые is a substantivized adjective. This means it functions entirely as a noun in the sentence (the tip you leave at a restaurant) but declines exactly like a plural adjective.

Is чаевые related to the Russian word for tea (чай)?

Yes! The concept of a tip in Russian historically comes from giving a worker a little extra money 'for tea'. That is why the adjective form of чай became the noun for a gratuity. It is almost always used in the plural (чаевые).

Since чаевые is the direct object here, why doesn't its ending change to show the accusative case?

It actually is in the accusative case! Because чаевые is grammatically an inanimate plural adjective, its accusative form is identical to its nominative form. If it were an animate substantivized adjective (like взрослые meaning 'adults'), the accusative ending would change to match the genitive case.

Wait, shouldn't the verb брать (to take) conjugate to something like брает?

Брать is a common but irregular verb that B1 learners need to watch out for. In the present tense, its stem changes from бра- to бер-. It then takes standard first-conjugation endings, making the 'he/she' form берёт.