Learn Dutch: De student betaalt de koffie. - The student pays for the coffee.

In English, we say someone 'pays for' something. In Dutch, the verb betalen (to pay) can take the item being bought directly as its object. You simply say betaalt de koffie (literally 'pays the coffee'). No extra preposition is needed.

How do I change this sentence into a yes/no question?

You use verb-first inversion. Simply swap the subject (de student) and the verb (betaalt) around. The question becomes: Betaalt de student de koffie? (Is the student paying for the coffee?).

If I make this a question, do I drop the -t on betaalt?

No, you keep the -t here. The rule for dropping the -t in questions only applies to the second-person singular pronoun (jij or je). Since de student is a third-person subject (like 'he' or 'she'), the verb keeps its standard ending: Betaalt de student de koffie?

Why does the verb betaalt have a double 'a', when the dictionary form is betalen?