I've seen a lot of discussions on various forums explaining that we should talk to our subjects before taking their photo. This approach works well and can be very effective. But this method is not without its flaws, because it forces the subject to interact with the camera in a self-conscious way. Let's break this down.
There are two general approaches to street photography: a candid approach and an interactive one. The first is an attempt to capture the subject in way that does not influence the subject's behavior. In the second approach, the photographer is known to the subject and this awareness dictates how the subject behaves.
Interactive Photos
I call these kinds of street photos 'interactive' because the subject is influenced in some way by the process of their photograph being taken. The subject is always interacting with three things: the camera, the photographer, and the viewer. The interactive approach is much akin to breaking the fourth wall in cinema and other media. The subject is aware that they are being viewed, whether it is in the given moment by the camera and photographer, or in the future by the viewer. What makes the photograph interactive is that it causes the subject to become aware of themselves, in other words, self-conscious. This self-consciousness is not necessarily a negative characteristic. Some people are more comfortable with it than others. But it does create a layer of behavior on top of the 'grounded' behavior that is exhibited by a person who is not interacting with the photographer, camera, and viewer.
This is not to say that an interactive photograph is not natural, or somehow shows the viewer an artificial aspect of the subject. On the contrary, the emotions, expressions, and actions portrayed by a subject in reaction to being photographed are natural functions of a human being. Rather than being considered unnatural, a subject in an interactive photo is self-aware, or at the very least, aware of the photographer. This modifies their behavior accordingly. Certain photographers employ various styles of interactive street photography, such as Bruce Gilden or Charlie Kirk.
Candid Photos
On the other hand, in a candid photo, the key difference is that the subject is not self-aware in the above sense. They are behaving as though the camera, the photographer, and therefore the viewer, are not present. Their behaviors are not filtered by their consciousness and modified for the benefit of the audience. This can be achieved in two ways: one is to utilize stealth or speed to catch people unawares. For instance, we can use a long lens (though I personally don't recommend this strategy). Another way is to shoot from the hip, from behind, or the side, or photograph people who are preoccupied in their current activity.
The second way we can achieve candidness is to ask for permission, take a few photos while interacting with the subject, and allow the subject to get comfortable with the presence of the camera and return to their 'grounded' behavioral state. This is where photographers such as Martin Parr are most at home. It's necessary to be outgoing and make your subject comfortable by talking to them. Once they are again acting as they would be without the presence of the camera, we can continue to photograph them while capturing truly candid moments.
Choosing a Path: Learn from the Masters
Which approach is better? Well, this is a wrong question in the Zen sense. Neither approach is right or wrong. Instead, the question we have to ask ourselves as photographers is this: what do I want to photograph, and what story do I want to tell?
On the interactive end of the spectrum you have the above-mentioned Bruce Gilden, who gets right into his subject's space and forces a reaction out of them. He photographs close and with a flash. It's nearly impossible for his subjects not to react. As I mentioned before, this does not necessarily mean we're not getting a real glimpse into the subject's psyche. On the contrary, the subjects immediate and visceral reaction to being photographed so abruptly illuminates their true character.
There are other times when interacting with your subject will result in more effective photos. For example, if you're doing street fashion, such as the work of Scott Schuman at The Sartorialist, then an interactive approach will let you work with the subject to create the most effective photograph for documenting each particular individual's sense of style. However, Schuman does also use a candid approach in some of his photographs, as it's not always necessary to pose and stage a good fashion photo.
I mentioned Martin Parr above—another photographer who employs both styles. He starts with a candid approach, getting very close. Once the subject is aware of him, always smiling, he speaks with them, making jokes. This puts the subject at ease, allowing for more photographs, some of which are more honest than the candid shots. You can see him at work in this video.
Finally, on the far candid end, we have photographers such as Joel Meyerowitz. His style is one of an invisible observer. His subjects do not pay any attention to his camera or his presence. He gives us as close to an impartial, unadulterated view of his world as we can get.
With this in mind, it will be easier to select a tactic or strategy for making street photographs. Good shooting!