"Did you find my ring?" you can use it if the action happened at some point in the past and no longer happening, meaning, the action of looking for your ring happened yesterday for instance and doesn't happen any more while you asking the question. "Have you found my ring" you can use it if the action of looking for your ring is still happening while you asking the question OR has just stopped a while ago before your question. More examples: Have you seen the last episode Prison Break? it means that the episode is still available in one way or another to see it if you haven't seen it yet. Did you see yesterday last episode of Prison Break? It means it's not available now in any way to see it. But who knows it may be will be available at some point in the future.

Where the verb? "What is the difference?" Use "Did you find my ring?" to ask about a past situation. (past simple) Use "Have you found my ring?" to ask about a present situation. (present perfect)