Sure thing. I got permission for a great house last week. I always try to dress nicely. I knock on the door, stand back toward the top step and wait for them to answer.
When they do I say something like "Hi, my name is Eric and I'm a bit of a local history buff. I'm in town visiting from Seattle today and was doing some research on the neighborhood. I thought I saw online that this house is from the 1880s, do you know if that's true?"
Then they usually say something like "Yeah, that sounds about right. What can I do for you?"
Then I explain, "Great, I have this hobby of metal detecting. I enjoy looking for old pocket change, tokens, and buttons. Would that be okay if I metal detect your yard?"
Usually I'm just looking for some kind of response at this point. If they are skeptical I might mention a neighbor I know. If they are still really turned off, it's probably better to just move on. Most people are cool with it but if you get a tentative yes, you are going to be looking over your shoulder the whole hunt and not truly enjoying yourself.
I then usually say "I'm happy to show you what I find. If I find any personal valuables like a ring I'd love to work with you to get it back to the owner." People love that.
If they ask about splits because they think you're going to find something great I say "I'm happy to go 50/50 with you on anything valuable I find." I've yet to find anything valuable enough yet that any of the owners truly care.
Hope that helps!