Learn German: Wir wollen ein neues Zelt kaufen.

Zelt (tent) is a neuter noun (das Zelt), and in this sentence, it is the direct object (the thing being bought), so it is in the accusative case. When a neuter accusative noun follows the word ein, the adjective in between must take the -es ending.

Why is the verb kaufen at the very end of the sentence?

This is the standard rule for modal verbs like wollen (to want). The conjugated modal verb takes the normal second position in the sentence, which pushes the main action verb (kaufen) all the way to the end in its basic infinitive form.

I learned to use möchten for "want". Why does this sentence use wollen?

You use möchten (would like) to be polite, especially when asking someone for something directly, like ordering food. wollen expresses a stronger intention or plan. It is perfectly fine here because you are just stating your own plan to buy a tent, not making a request of the listener.