Years ago when I was young I took a job selling vacuum cleaners door to door. After a very successful year, income wise, the knocking on doors finally got to me. Little did I know that years later that unwanted talent would come back to serve me.
Now, selling door to door and asking permission to metal detect are two entirely different things. But, you can learn a few things from selling.
First, be positive. If you go to the door and say something like, "You wouldn't want to let me metal detect your yard would you?", then you don't have to guess what the answer will be.
Second, be neat and courteous. I know that after you have been hunting a few hours you can get dirty and sweaty. But you can tuck your shirt in and comb your hair before you get to the door. Knock and stand back a way from the door to make them comfortable with you being there.
Third and most important, be honest. Don't use any gimics or off the wall ideas when you are at the door. Just simply introduce yourself and say that your hobby is metal detecting and that you would like to get permission to hunt there (in so many words - short and to the point).
The next part is a very important part that I learned from selling. After you ask them permission, do not say anything until they answer. It might seem like you are waiting there for 10 minutes, but be silent until they answer first. The longer it seems, the better your chances of getting in.
In selling, it is called the "silent sell". Why it is important is because many inexperienced salesmen/detectorists during this critical time will continue to talk and end up talking themselves right out of a sale/hunt.
So say the brief lines I mentioned above, then wait for the answer. If the answer is "no" then thank them and move to the next potential site.
If the answer is "yes" then this is important as well. Thank them and again keep quite unless they engage you in conversation. For the same reason as above you can talk yourself out of a hunt. My buddy that I hunt with is 78 years old and is deeply afraid to knock on a door, so I usually do all the knocking. Other than that, he runs his yap more than any woman you will ever be around.
One day I got permission for us to hunt, and was in the part of being quiet and starting to hunt when he gets out and starts trying to sell what I had already sold. I'm talking about a 160 year old house here. He starts talking about not leaving holes and returning any jewelry we find, etc.
Well, you guessed it, they changed their mind about letting us hunt. So once you get permission, shut up and hunt.
When you are through, go back and tell them you are leaving and thank them for letting you hunt there.
Just like in sales, you have to go through so many "No's" before your get a yes. They used to say it is a game of numbers. You should look at getting permission the same way. Or you could look at it like swinging your coil or finding pull-tabs. If you swing long enough and dig enough pull-tabs, sooner or later you will find gold. If you don't swing your coil and dig pull tabs you will never know what you missed.
The same is true of not knocking.
Lose your fears (and doubts) and knock, it is just one more step to your next great find!
BTW, my success rate of getting permission is 85-90%. This attitude also overcomes the problem of "No Tresspassing" signs since you are not tresspassing if you have permission. In fact, it has provided quite a few really good hunt sites to me that others never bother with. Getting permission is a good thing. Use it to your advantage.
HH Alton