Holding the camera
Holding the camera properly is the best way to avoid or minimize the effects of camera shake. A good firm grip with the right hand and support from underneath means that, when you press the shutter release, movement of the camera will be minimized. This will enable you to shoot sharper pictures at slower shutter speeds.
The picture on the right shows a good grip, the heel of the left hand supports the camera from underneath. When the shutter is pressed with the right hand, the camera tends to move downward, the left hand in this position will minimize the effect of this.
Some older cameras had shutter buttons that pushed in towards the body instead of downwards, but they seem to have largely disappeared nowadays, presumably because the position did not feel as comfortable as the downward movement.
Cameras were designed to be used with the right eye, although it is possible to use them with the left. The advantage of using the right eye (which feels more comfortable to most of us anyway), is that the left eye is not blocked by the camera body and you can, if you want, keep it open to see what is going on outside of your field of view. The natural tendency is to shut your left eye, the better to concentrate on your picture, but with a little practice, you can get used to keeping it open. Having the left eye open enables you to see what is about to move into your frame, a useful thing when taking action shots. Also you can see what happens at the time when the exposure is being made and the mirror is blocking your view in the viewfinder. Did the person you are photographing blink? Better check and take another shot.