One trick that I use straight out of the psychology of persuasion that always seems to work is bring a small gift for the property owner. I give this right up front, usually a couple coins that I've found somewhere that don't hold much intrinsic value, Indian heads, etc. then I lead into that as an example of some stuff that I may find if I'm lucky. Sometimes I see a property I didn't plan for and I'll grab a dozen donuts, or take a look at the property for some cues on what will make a good but cheap small gift. Make sure you give it up front after introductions, and don't take it back. They'll always try to give it back, and I always say it's a small gift and the least you can do for taking up their valuable time talking to you briefly.
The psychology behind this is that we humans can't stand the feeling like we owe something back, so granting permission to hunt on the spot is a no-brainer. Also, the act of gift giving sub-consciously increases that property owner's feelings of likability towards you.
Don't use the word dig at all. I replace dig with extract, and offer to show them how I "pull a plug" so that their property looks exactly the same as you left. Don't door knock after a long day of detecting and generally watch your appearance. Older men especially will judge you at face value for things like sloppy appearance, tattoos, shirt not tucked in, ripped jeans, etc.
Last but not least, do yourself a favor and spend the couple bucks to have business cards printed with your contact info. If you don't want your personal phone number on it or email, just create a new gmail address for seeking permission, and after you get that email sign up for a free Google Voice account. You can use the Googke Voice app on your smartphone, or set it to forward calls to your regular email. Lead all opening conversations with your business card. You can also get yourself a custom logo for $5 on fiver.com.
Just my .02 for what works great for me. Your mileage may vary.
