You may remember I snapped Bruce Gilden here in London in full action. I don't like his style, but he has sphericals of steel. However, he is at the extreme end.
I am at the stage now where I am comfy enough to raise the camera, snap and smile if eye contact is made.........then walk swiftly on.
I had some cards made describing who I am, what I do and where you can find my work. I also have my iPhone with my best and most complimentary street snaps on it which, if necessary, I will show.
I was challenged by a guy last week who said "did you just take a photo of me"? I looked hard at him and said "nah mate....not interesting enough" took the wind out of his sails completely.
My view is hide in plain sight. Don't sneak as you just draw attention to yourself. I find that the closer I get......the less they see of me. Don't underestimate knowing your camera. Hold it in the most comfy position at hip and whatever level you use and see where the lens points. Make it your corporate style so that you can position yourself correctly when you spot something interesting. I know intuitively where my lens is pointing and what my field of view is most of the time now. My hit rate is far superior to what it used to be.
I am really only a beginner in comparison to some of our esteemed forumites........but this is what has stood me in good stead.