I'm often asked about how to shoot 'from the hip', which is a euphemism for taking a photo without looking through the viewfinder. Sometimes it's from the shoulder, sometimes from the middle of my chest. There's no easy answer, but several things are important to consider.
1) Exposure needs to be set. I usually have my camera on auto ISO and set the aperture and shutter manually. You need to be able to read the light and set them without looking at the exposure information in the viewfinder. When I'm walking around shooting I'm always aware of changes in the lighting. When I turn a corner I take a quick reading and adjust my camera accordingly.
2) I use fixed focal length lenses on the X-Pro1. When I used the D700 I usually had the 24-70 f2.8 zoom on the camera, but 90% of the time the lens stayed at its widest focal length. On the Fuji I most often shoot with the 18mm (28mm equivalent) except when I'm sitting in one spot in which case I use the 35mm (50mm equiv.) I'm chomping at the bit waiting for Fuji to release the new 14mm lens. It's important to keep the focal length in mind because you need to be aware of the area of coverage that you will get without looking through the viewfinder. That's why wide angle lenses work best for this type of work - they maximize the environmental information in the shot.
3) It's important to be aware of what the lens is focusing on. If you take shots like those below where the main subject is off-center, but the autofocus is set to concentrate on the center of the frame, you either need to use a very deep depth of field, focus and recompose the shot (very difficult to do when shooting this way), or adjust the focal point of the camera (also very difficult to do). I've become somewhat adept at anticipating this problem, but it's taken many goofs to hone my skills.
4) One of the most basic techniques that needs to be mastered is to understand how to tilt the camera up or down so that you don't chop the top of someone's head off in the shot, or have half a frame of sky (negative space) and a shot of someone from the neck up. Once again, this takes practice and quite a few missed shots.
5) Avoid the impulse to chimp. When I began shooting without looking through the viewfinder, I always wanted to see if I 'got' the shot, and if not, make the necessary adjustments next time. The problem is that you run the risk of missing another shot while you're looking at the LCD on the back of the camera. It may be necessary at first, when learning to shoot like this, to check the image. But now when I'm out on the street I never look at what I've shot until my train ride home.
All that said, there are plenty of times I use the viewfinder too. Part of the pleasure I get from shooting with the XP1 is the Optical Viewfinder experience - the opportunity to look through the viewfinder and see a scene as it unfolds before you, to see people before they enter the area of the frame. If I know a person will be receptive to my taking their photo, I spend a little extra time to compose the shot and get everything exactly right.
Both of these shots were 'from the hip'.