Once you get a name and address, I can tell you a way NOT to do it: Don't send a letter, and don't make a phone call. Because think of it: What do YOU do with junk mail from total strangers? Throw it away, right? And what do YOU do when you get a phone solicitor? Hang up, right? And another thing, don't show up with search and salvage type agreements/contracts (types are commonly seen from time to time on web md'ing forums). Because think of it: What would YOU do if a total stranger showed up on your doorstep with a contract for you to sign? The only thing that would do is conjur up images of some sort of legal hassles, and would be detrimental to your goal.
Better just to show up in person, with a friendly smile. Try to catch them on their porch or out in their lawn, rather than knock on doors (as "bumping into them" is less threatening than knocking on doors) if you can. Be sure to have your detector in hand, as this helps with the mental image of what you are asking. Otherwise, sometimes you're left trying to explain the concept of a metal detector, blah blah. But if it's right there in your hand, you've got a picture for their minds. Be sure to have some grubby wheaties and merc or two that "you found down the street at the park or school", to put an image on your goals (that you are innocently looking for pocket change, blah blah as your hobby). Be sure to have your old maps in hand, as this often interests land-owners, to be looking at something, about their own property, that perhaps they haven't seen before. I have often-times found myself in lengthy conversations with landowners, who are excited to tell me what they know about the old stage stop, or whatever it is, that I'm asking about. When they see that I've got the details about the history of the stage stop (or whatever) down, then they will chime in with things like "my grandfather tells me that the outhouses were over there, and the black-smith shop was behind there, blah blah". In this way, if you present yourself as a history buff, that sometimes comes off better than "treasure hunter" or whatever.