I look at creating my images as a two step process: getting the shot, then processing it. I have a good idea of the processing steps I will take the image through once I upload it to my computer, and that to a great extent defines how I go about shooting. For instance, I know what I can and can't do to control and adjust the light and shadows of a scene so as I walk along looking for shots I try to visualize what the final image should look like. That holds true for the focus, aperture, and horizontal/vertical composition.
For now I'll deal with just the first step - getting the shot. I don't often go out shooting with other people. When I'm not alone I generally end up with either no pictures or lousy ones. It's distracting and I can't stay focused on what's happening around me when I'm chatting with someone. I try to avoid having people 'tag along' so they can watch me work (because, they say, they want to see how I do it). That makes me way too self conscious, and they often get in my way when I want to move in a certain direction to get the shot I want. And most importantly, I like to be alone. When I'm alone with my camera and out on the street I get buzzed, and I don't want to share that with anyone. It's too good.
Sometimes I go out with people to instruct them. For that, I have my camera with me but there's no pretense that I'm out to take my own shots. I watch what they do and talk about their technique and approach to shooting. The first mistake almost everyone makes is having the camera hang around their neck or over their shoulder, or at their side in their hand. It's a mistake because if you see a shot and the camera isn't instantly ready to take it, by the time it is ready the shot is gone. Or just the action of picking the camera up and aiming it will draw attention and ruin the scene. Unless, of course, you're far enough away from the subject and shooting with a longer lens so that the subject doesn't see you. In which case - you're too far away from the subject to get a great shot anyway. Cornell Capa's maxim was that if your pictures aren't good enough, it's because you aren't close enough. That may sound like an oversimplification, but it's the second biggest mistake photographers make in shooting street.
Street opportunities are like quantum particles, spontaneously popping in and out of existence. If you don't have time to pick the camera up, and you're right on top of your subject, you certainly don't have time to fiddle with buttons and dials. You need to have the camera set to make the correct exposure with the correct aperture, shutter speed, and ISO to get a good exposure, and the depth of field you can work with.
So, given all that, what do I do? Firstly, what I don't do is worry about whether I should or shouldn't take a person's picture. I'm not an attorney so I can't offer this as any kind of legal advice. I do not use my images for commercial purposes. They are editorial, so I do not need to have a signed release. In the United States of America if a person is out in public they have no right to the presumption of privacy. I can take their picture. If they are aware that I have taken their picture (most often they are not), they might get pissed off and say nasty things, but that doesn't bother me. Only a few times have I ever had a physical confrontation. If that remote possibility is a problem for you, don't shoot street.
Secondly, I keep my camera in front of me at the middle of my chest with my hands wrapped around it and my finger on the shutter button. The zoom lens is set to 24mm, the shooting mode is set to continuous - high, the focus mode is continuous, and the exposure mode is aperture priority/auto ISO. I adjust the aperture depending on whether I'm in bright light or shadows, always paying attention to what will happen to the depth of field with whatever aperture I choose. Setting the lens to 24mm gives me the widest area of coverage with my regular shooting lens (usually when I go out to shoot street I take just that one lens. I don't like to be weighed down by a heavy camera bag with stuff I'm not going to use anyway).
Thirdly, when I see a shot about to happen I get into the best position I possibly can as I walk towards my subject, and I fire off a series of three to five exposures as we approach each other. I've practiced this enough to know how to hold the camera to get the proper axis for the lens and I can get pretty close to the composition I want for the image without having to look through the viewfinder. That gives me the advantage of 1) not having to draw attention to myself by raising the camera to my eye and 2) seeing the action all around me as it unfolds.
As I was walking up Eighth Avenue (with my camera in front of me and my finger on the shutter) I saw this gentleman who was smoking a cigar approach me. I love cigars. My eye was immediately drawn to him. I wanted the shot to look threatening, and it worked out great because he's got that hat shadowing his eyes, looking right at me (me, of course, not at all looking at him directly), and everyone else in the scene has their backs to the camera which isolates that one gentleman facing me. I fired off several frames as we passed each other. This was the only one in which he was looking directly at the camera, and of all the shots this particular one required the least amount of cropping. The image came together beautifully. Nothing to it.
Processing, however, was a whole different story.