I don't ask permission - I just make my photographs.
I've made thousands of street photos and have never been badgered or threatened physically. I have had questions or discussions with subjects about why I photographed them. When people ask questions, I explain what I'm doing and show them some street photography prints which I always have in my camera bag. This shows them I'm a "real photographer" and I'm not doing anything wierd or unethical.
I've hardly ever been "caught" but it does happen. When I get "caught," it's because I have gotten careless or had a lapse of concentration. I view getting "caught" as a shortcoming or a failure on my part.
In some situations, I will ask parents if it's okay to photograph their children - sometimes I just make the photos. It all depends on the location, situation, circumstances and demeanor of the parents and the children. With time, you seem to develop a sixth sense about this.
I photograph in such a manner that people rarely realize I'm photographing them. I use a 28mm lens on a 35mm rangefinder, so I have to get close - anywhere from arm's length to eight or ten feet, depending on how much background I want and how much of the frame I want the subjects to fill. With one or two people, I want them to fill 1/3 to 1/2 of the frame so I have to get pretty close with a 28mm lens.
How do you get to within three or four feet of your subject and not get "caught"? You get your subject to ignore you.
It's all in the way you physically approach your subject. You approach slowly and discreetly. You look around, at anything but your subject. You "dance" to fine tune your composition - subject sees you, look at camera and pretend to fiddle with it, sujbject looks away, a foot closer, six inches to the left, look away, look thru your viewfinder at something else, six inches closer, your subject is distracted and not looking at you and *click* you have your image. Look away, wind film, reframe, *click*. Six inches to the right, *click*. Lean in six inches, *click*.
Using ISO 400 film at 1/60 and f/11 (in open shade) makes this possible; you don't have to focus and you have depth of field from 3.5 ft. to 12 ft. or 4 ft. to infinity with a 28mm lens. In direct sunlight, you can shoot at sunny 16 with ISO 400 film (1/500 @ f/16) and have depth of field from 3 ft. to infinity.
Henri Cartier-Bresson did this "Leica dance" when he did street photography. It worked then and it still works today.
HCB also said something to the effect that street photography was a game of millimeters - and it is.