Step one is to be there. That is the most important thing. I always keep a quote by Chuck Close in my mind when I'm not shooting, when I'm sitting at home and contemplating whether or not to get out of the house. I'm paraphrasing but it goes something like this: "Creativity is the product of curiosity and rigor." Curiosity gets you out of the house and going to specific places—likely places you have never been to before. Rigor gets you doing this consistently, even when you're shooting bad photos and feel discouraged. To get the good shots, you have to be there.
With that out of the way I do have a few specific techniques and ideas to keep in mind when shooting people in the streets. Since we already covered the first step, we could call this step two. Step two is to know your gear and be comfortable with it. Shooting needs to happen instantly without any fumbling with your camera. It should always be ready to shoot and set in a way that allows you to react instantly. When the camera is in your way, it hinders the creative act. But when you become 'one with the camera' it enables you to create effectively. So you must know your gear's quirks well and how to compensate for them. For example, my camera often overexposes on cloudy days. So I know to set the EV to something like -.7 when it's overcast. Another thing you can do is preset your manual focus lens to a certain range and shoot subjects at that range. This is called zone focusing and allows for some very fast composition.
Which brings us to step three: composition. The word 'composition' comes from the discipline of painting. This is a bit out of line with what we do as photographers in the streets of a city, since we can't add or remove elements the way a painter can. Another way to look at composition is to consider the subject's isolation. When framing, we can try to isolate the subject and bring focus to them by removing elements from the frame. This is a matter of timing and positioning. It doesn't just have to be taking away elements however (otherwise we'd all just be shooting our longest lenses at f/1.4 to bokeh out everything but the subject). Certain elements are necessary in the frame to provide context, which in turn gives us a story. The decision to keep or remove these elements is often limited by circumstance, but it's something that should be kept in mind.
So how do we tell a story with a photograph? Well a good story needs characters. Step four is to create characters. Notice I don't say 'find characters' but rather 'create'. Now I'm using this word loosely because you don't actually go out and create people. But we can use our framing and timing to decide when and how to take the photo. I want emphasize this point because it's really discouraging to wander the streets waiting for something to happen, since sometimes it never does. What's important is to keenly observe and find moments when a person on the street becomes a character, when they express their soul and emotions in a subtle or not so subtle way. This might be a vague way of looking at it, but it's what separates a boring photo of a random stranger from a fascinating photo of a human being.
To bring it all together the last step is to anticipate and make predictions about the scene. In many ways urban photographers must react to what's happening around them. This doesn't give you much time to compose the frame, so every extra second counts. If you see a woman about to step or jump over a puddle, you should get ready to take a photo. People are spilling out of the train station during rush hour? It might be a good idea to get into a good position and wait for something to happen. Think of yourself as a wildlife photographer. Many times it's necessary to lie in wait and let the subject come to you.