"Howdy, Neighbor- I'm Jeffro, I just live up the street there... I was wondering if it'd be possible to run my detector over your grounds sometime? If there's anything you've lost over the years I'd be happy to search for it as I go. (Not for new arrivals, LOL)
"Also, if you'd like me to try and track down where you water main, electrical, etc. runs; I'd be happy to do that as well. If I can get a good enough signal, that is." (Older houses have galvanized pipe, sometimes not near as deep as todays codes)
Chit chat, introduce yourself, and look presentable before you go a knockin'. Be pleasant and confident. Welcome them to the neighborhood, if new.
Best not to bring your detector to the door, as if your expecting them to say yes....
Also expect to hear a no, and don't be disappointed if they do say no. If they do say no, just say, "Well, if I can ever be of help in the future, let me know."
Simple business cards to leave with them can help sometimes, if they decline ,but show interest in what you're doing. Nothing but name, address, phone number, and "metal detectorist", with maybe a logo of a detector on it.
Alot of people get a lot of "Nos". I think it has to do with confidence and personality, more than anything else.
Don't pick out houses with well manicured lawns, in general. The type neighborhood you want to detect in has a lot to do with responses, too. High crime areas will generally be No, but rural communities and suburbs are more likely to say yes.
Don't forget to wave and say Hi! as your driving by and see them in the yard someday. But don't press your luck by asking twice, let them come to you after you've proven yourself to be a decent type fella.
Pretty much common sense stuff. Hospitable and pleasant. Try it in front of a mirror, or your wife first and see what you can pin down, change or leave out. Genuinely mean whatever it is you decide to say. If you don't, you'll come off like a used car salesman.
Hope this helps.