Many digital photographers tell me they have trouble getting sharp pictures with their new cameras. There are two things that likely contribute to this.
First, because of that alluring LCD monitor on the back of the camera, we now frame our pictures by holding the camera away from our body so we can see the photo in the screen. It's much harder to hold anything steady at arm's length rather than close to our body. So if you have a digital camera with a window or electronic viewfinder (a miniature LCD screen in the eyepiece), try framing your picture by looking through the camera traditionally...with your camera pressed against your face. This will steady the camera and give you sharper photos.
The second likely cause of blurry photos is related to the shutter button. All autofocus cameras (and that includes all digital cameras) have a two-stage shutter button: halfway down and all the way down. When you press the shutter button halfway, you are asking the camera to prepare to take a photo. The camera's computer focuses the lens, adjusts the exposure and color, and maybe even charges up the flash. When the camera is ready to take a photo, it alerts you with a beep. It may also show a steady green or orange light next to the viewfinder (green for no flash, orange for flash) or green squares on the LCD monitor. Then you can press the shutter button the rest of the way down to take the photo.
If you practice this halfway down and all the way down on the shutter button, you will not only get sharper photos. You will also speed up the camera. By preparing the camera before you take the picture, it will be all set to capture the moment when you press the shutter the rest of the way down.