Everything in photography is about light. Many people complain about blurry images and the amount of available light has everything to do with it. If you can get away with using a flash, that’s a sure-fire way to get the job done. Keep in mind that most point and shoot cameras have a flash that will only reach to about 13 feet. If you’re using an SLR, the camera’s built in flash will give you a very similar light output. If you can afford it, it would be wise to invest in an accessory flash unit. A high-end flash can give you up to 80 feet of distance and will cost you around $500. In addition to drastically reducing blur, an accessory flash unit will also help in reducing red-eye.
Another thing that can help you is image stabilization – but there’s a catch. Image stabilization (or vibration reduction or steady shot or vibration control… it’s all the same) will help control blurry images caused by camera shake. If your subject is moving they’re still going to end up blurry. If you’re getting camera shake and you don’t have image stabilization, hold the camera with both hands while holding your arms against yourself – essentially forming a tripod. It’s not a 100% solution, but it should help.
Some small digital cameras have something called “E.I.S.” or “Electronic Image Stabilization”. EIS essentially raises the camera’s ISO (or light sensitivity) in order to capture a less blurry image. In doing this, it is also lowering your image quality and creating a lot of noise, or grain, within the image. I would only recommend doing this if it’s completely necessary.
The only absolute solution for blurry images is to increase the amount of available light, though of course in many situations this is not possible. Get creative if needed – then you’ll get the best results.