Most people have trouble with newer cameras blurring. This is because the megapixel size keeps increasing and people really don't need images that large. Here's a few tips for casual photographers"
1. You can lower the mega pixel size, you should have this option, and or lower picture quality which should be smaller size, but leaving it in full size will print nice 8x10's or larger. If you don't need that large lower the mega pixels.
2. Set the camera on sports setting, or kids playing setting if you have that, some cameras have both, but sports is the about the same - kids setting is more for indoors.
3. While in sports setting use the option to take more than one image with one click. When you take photos take several this way and then maybe some will be better than others.
4. Relax when you click and slowly push the shutter and make sure you don't jab at it if this is the case.
When you use sport setting, and when you use the multi picture per click option your image size will automatically be smaller. You are probably using auto setting and that is larger image size.
Having said all that I don't do any of that, I use manual modes. I just hold it steady or use a tripod. But when under pressure it is easy to miss a shot so first use sports setting and maybe turn it to auto and see how it turned out. Hold the camera in a way that you brace you arms against your body or rest the camera against something like a book case, doorway or something. Use the eye piece instead of the lcd, it will hold steadier resting against your face with arms against your body.
Taking photos indoors - the camera shutter has to be open longer to absorb more light so the darker it is the more blurry photos you will get. To avoid this you need better lighting, or use a tripod. No one can hold a camera without shake for 2 seconds, not even a split second. Go outdoors if you can, turn on more lights or set the camera on something, maybe someones shoulder but a tripod is best for indoors, even with flash.
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