A monopod or small tripod will help. If it's not a heavy camera you can get a little tabletop tripod for under ten bucks.
If you just have a little point-and-shoot, get the cheap tripod, but also try taking pictures in brighter light. That'll force the camera to use shorter exposure times, which means less movement will be picked up in the picture.
If you have a DSLR, you can deliberately choose shorter exposure times, and figure out which one is the shortest you can use under given light conditions. You should be able to select the ISO. This is a relic of film days but essentially a higher ISO means greater light sensitivity. So if you use a higher ISO you can get away with shorter exposure times, which again means less shake will show up in the picture.
If you use a tripod rather than a monopod, figure out where your camera's timer setting is. Use the timer so that you can press the button and then take your hands off the camera. Then when the picture is taken you aren't even touching it. Even cheap point-and-shoots have timers, quite often. Some cameras also support remote shutter triggers; either you can get a cable that screws on to the shutter button, or it might have come with a little wireless shutter button on a remote control. Either of these can be used with a tripod to reduce or eliminate the problem of your hands touching the camera.