I observe the person carefully and see why I want to take a photo of this person. For a woman it may be a beautiful face, fashionable clothes, nice hair style, large expressive eyes, etc. For a man it may be handsome face, muscular body, a face with distinct character, etc. If there is no compelling reason to photograph the person, I just move on. I dont want to waste my time or theirs.
I just look at them and smile genuinely. If they smile back or at least look neutral (not hostile), I tell them 'you look beautiful' or 'you have very good fashion sense', or 'you have a lovely hair', etc. There is a 30% chance they walk away at this stage. No problems.
If they dont walk away, I say, 'I am a photographer. I would like to take a photo of you. It will take just 2 minutes. I will email you the picture.'
There is a 70% chance he or she will walk away at this stage. No problems.
If they agree, I go ahead and take 5-6 shots from 2-3 angles. Not more than 5 minutes. After that I give them my name card and take down their email.
The important thing is not to take rejection personally. They are not rejecting me as a person or as a photographer. It is just that don't want their photo taken by a stranger.
Most people are shy by nature. Sometimes it is just that they are not in the mood to give smiling poses to a stranger. And then there are some people who are genuinely scared of strangers! Whatever is their reason, I accept it gracefully and walk away with a smile.
As they say, there is plenty of fish in the sea. So, I move on to the next subject.
Good luck...
Sam
www.samkumar.com