That Sony cybershot doesn't have any form of image stabilization. A lot of pocket cameras don't. If you're having a lot of problems with hand shaking causing blur, there's only a couple of ways to fix that.
First, is to get a camera with good image stabilization. The quality of IS between camera's varies, but if you stick to Sony or Canon you're going to get good results, as they've been leading the pack for IS functionality. Nikon is also a safe bet, but IMO their IS isn't as good, with the exception of their new DSLR's with built-in IS. Pentax has an affordable DSLR with built-in IS that's popular for that reason alone. For point-and-shoot cameras, there's a wide range of options, and you'd need to provide more specifics on what you use the camera for to get a proper recommendation. Although I'd personally recommend the new Canon SX100, it's a nice size, can be pocketable, has 10x optical zoom, and top class optical stabilization, equal to 4 f-stops of exposure.
Second, is to learn better photography techniques. Lock your elbows. Breathe out while taking the shot. Prop your hands against a firm surface for stability. Learn how to adjust the ISO, shutter speed, and aperture of your camera for your current lighting conditions.
Camera's are remarkably limited compared to the human eye and brain, it can be a real struggle to get good shots routinely. Getting crisp shots in a variety of poor conditions, low light, fast action, etc., is what drives most people to upgrade to DSLR's, and learn more about the science of taking good pictures. It's a lot to learn, but it's totally worth it when you can capture the soul of the moment and bring it out the way your mind remembers it.
