I read this tip somewhere I can't remember where but I will try to pass it on as simply as possible. It is not difficult believe me. It just needs a bit of courage and practice.
When we shoot subjects (not people) in the streets, we tend to immediately look at the screen of the camera to see the result. If you are shooting people in the streets you want to do the opposite. Shoot those people and try not to remove the camera away from your eye. Keep pretending that you are shooting the background and leave your camera there as the person walks out of the scene then look at the screen. When that person think that you took their photo and look back, they see a photographer with the camera still composing the scene and their eye locked in the viewfinder. "Ah he is not taking my photo, he is a tourist most probably shooting that monument / building / background..." At this stage they will likely keep walking, thinking that they were just in the way.
Another advice is to start aiming up above, or to the sides of the person, like I am photographing a building or a nice background. I will pretend to take an image or two, and then at the last second I will move the camera so that they are in the scene, in the right composition.
Go ahead and try it the next time you wonder in the cities. Don't be afraid and shoot them all! Don't forget about Henri Cartier-Bresson's decisive moment however...