The shutter speed, which ranges from long/slow shutter speeds (like a half second, one second and even longer) to fast shutter speeds (like 1/125th, 1/250th and 1/500th), controls how sharp the picture will be because it can freeze motion from the photographer handholding the camera as well as movement from the subject. So, to eliminate both of these movements as much as possible, you should choose a fast shutter speed.
What constitutes fast? For a quick-moving subject (like a running athlete or a dancer), “fast” may be 1/500th of a second or quicker. For a normal portrait, for instance, or a basic daylight landscape scene, “fast enough” may be 1/125th or even 1/60th, the latter of which represents the generally acceptable slowest handholdable shutter speed—meaning that if you’re going to use a shutter speed slower than 1/60th, you should mount your camera to a tripod. Take a look at the example of the duck shown here, which shows how much camera shake ruins a picture at a slow shutter speed compared to a faster one.
Another factor in choosing the correct shutter speed is lens focal length. The longer the lens, the more it amplifies every little shake and jitter your hands make, so the faster your shutter speed needs to be to counteract that movement. A good rule of thumb is to use a shutter speed as fast as the lens’ focal length in millimeters. So, a 1000mm supertelephoto lens would require a shutter speed of at least 1/1000th of a second to remain sharp during handholding. The good news is that means a 50mm normal lens only requires a shutter speed of 1/50th or faster.
If you want to eke out every advantage you can while handholding, consider investing in two pieces of equipment: an image-stabilized (or vibration-reducing) lens and/or a mirrorless camera. The former uses tiny electromagnets to move a floating lens element in order to counteract the movement of the lens itself, and the latter has no moving mirror (as an SLR would), so there are no vibration-inducing moving parts during the moment of exposure. In practice, this means that photographers using mirrorless cameras report increased handholding capability, even if the effect isn’t nearly as dramatic as it is with a dedicated image-stabilizing lens.