Stay calm... and carry your camera everywhere
The best way to take spontaneous photographs in the streets is to always be ready to shoot. I have DSLR camera that I take out with me when I’m on a family outing or just when I go with my asssistand (my son) to take some landscape shots. But when I am walking on the streets I would like to shoot with a system camera or point-and-shoot (compact) camera that I can use without being noticed.
Use a telephoto lens
Obviously the further you are away from your subjects the less likely they will be to know that you’re photographing them and the more natural they’ll be. Others might argue that you should carry only one mid-range lens like the 18-55 mm but just be prepared for all situations and keep that telephoto lens in the car hidden somewhere in the trunck.
Don't use flash
The most obvious way to disclose yourself or to signal to anothers that you’re photographing them is to use flash. Attempt to photograph without the flash if you’re aiming for candid shots. Test your camera by increasing that ISO settings and use a faster lens, and open up your aperture. Hopefully one or a combination of these settigns will help you get camouflaged in the crowd or blended in the background.
Shoot more and use burst mode
Don't shoot once. If you take multiple shots of a person you are increasing your chances of getting a surprising or spontaneous shot. His/her eyes might be closed at the moment you release that shutter and you don't have a second chance to reperform. So switch your camera to drive / continuous shooting mode and shoot in bursts and in doing so you’ll increase your chances of that perfect shot.
Anticipation and position count
While street photography is about capturing the spontaneity of a moment or a social message, getting that perfect shot at the right split second of time is crucial. You don't want to be stationed behind the scene or in a bad perspective spot. Try to think ahead and anticipate what is about to happen on the street. Wait for that hobo to be located beneath a luxury street ad for example or anticipate that business women crossing the street while capturing the green light in the scene, etc. Consider each moment: which way will people be facing? what will they be doing? what will the light be like? when will they turn and face the camera?
Shoot people when they are engaged or doing things
Pictures of people at work or engaged with their daily routine tend to be much more interesting than people sitting doing nothing. This adds energy and context to the photo not to mention that you will be unnoticed if they are busy doing things. Timing is everything in street photography, so wait until they are distracted from you and fully focused on what they are doing.