It has become fashionable in the last decade to use handheld camerawork for a sense of drama and immediacy. A bouncy camera conveys realism and makes the viewer feel a little bit more like they are a part of the action. But a lot of people hate it, and for most situations it's best to keep the camera as steady as possible.
The easiest way to do this is not exactly a secret - use a tripod. You can pick a basic one up for as little as Â£20, although a sturdy model with plenty of adjustment options and useful extras like a fluid level head will be closer to Â£50. But even that is not much to pay for the professionalism it brings to your camerawork.
When you can't use a tripod, it's still worth making every effort to keep the camera steady. A simple way to do this is by taking the camcorder in one hand, then holding onto the wrist of that arm with your free hand, and making any camera moves with that arm instead. This will smooth out the motion. An alternative method is to hold the elbow of your camcorder arm with your other hand. You can also plant your elbows against your chest, and move your entire body, although this position is quite hard to maintain for very long! But it's worth doing for slow, steady pans or tilts. In effect, you turn yourself into a human steadycam!