Learn Dutch: Zij heeft een ring aan haar vinger.

In Dutch, the preposition aan is used when something is attached to, wrapped around, or hanging from something else. Because a ring encircles and holds onto the finger, you use aan. You would use op (on top of) for something just resting on a flat surface, like a ring on a table (op de tafel).

Since this lesson is about the general pronoun je (one/people), how would I write this to mean "One has a ring on one's finger"?

You would change the subject to je, the verb to hebt, and the possessive pronoun to je, making it: Je hebt een ring aan je vinger. This is the most natural way to say "You wear a ring on your finger" when speaking generally about people.

Could I use Ze instead of Zij in this sentence?

Yes! Ze is the unstressed version of "she" and is much more common in everyday speech. You use the stressed Zij when you want to put emphasis on the person. For example, to point out that she has a ring, but someone else does not.

Does haar change if the subject Zij means "they" instead of "she"?

Yes. If the subject is Zij meaning "they" (plural), the verb becomes plural (hebben) and the possessive pronoun changes to hun (their). The sentence would then be Zij hebben een ring aan hun vinger.