Learn Russian: Мы хотели бы ещё один стакан сока, пожалуйста. - We would like one more glass of juice, please.

хотим means "we want", which can sound a bit direct when ordering. By using the past tense хотели plus the particle бы, you create the polite conditional mood ("we would like"). This is the standard way to make a polite request in Russian.

Why do we use ещё один to mean "another"?

In English, we often say "another glass", but in Russian, you literally say "still one" (ещё один) when you want an additional item. If you used the word другой (other/another), the waiter would think you want a completely different glass, perhaps because yours was dirty.

Since "a glass" is the object being requested, shouldn't стакан be in the Accusative case?

It actually is in the Accusative case! стакан is the direct object of the sentence. However, for masculine inanimate nouns (objects, not living beings), the Accusative form looks exactly the same as the Nominative dictionary form.

Why is the word for juice spelled сока here instead of its dictionary form сок?

It is in the Genitive case, which often translates to "of" in English. When you are talking about a container holding a quantity of something, the substance goes into the Genitive case. So, стакан сока literally means "a glass of juice".