Learn German: Möchten Sie zusammen bezahlen? - Would you like to pay together?

This is because of the modal verb möchten. In German yes/no questions, the modal verb goes first. The main action verb (in this case, bezahlen, meaning "to pay") gets pushed to the very end of the sentence in its basic dictionary form.

What is the difference between "möchten" and "mögen"?

While mögen means "to like" in general, möchten means "would like" and is used for polite requests or current desires. A waiter uses möchten to politely ask what you want to do right now.

Why is "Sie" capitalized here?

Capitalizing Sie makes it the formal "you". In German culture, service staff like waiters and cashiers will almost always use the polite, formal Sie with adult customers instead of the informal "you" (du or ihr).

Why does the verb "möchten" end in "-en" here?

The verb ending always has to match the subject of the sentence. Because the subject here is the formal "you" (Sie), the verb takes the -en ending, which makes it look exactly like its infinitive (dictionary) form.

If I don't want to pay "zusammen", how do I say I want to pay separately?