If you're shooting in the full Auto mode, you are not taking advantage of the capabilities of your digital SLR. Your pictures are blurry because the shutter has to stay open long enough to properly expose the picture, but the people are moving while the shutter is open. You need to increase your shutter speed or increase your ISO, which means you have to select another mode on your camera. You could invest in a "faster" lens, which means that it can allow more light into your camera, but is also more expensive. Try this excellent tutorial on using a digital SLR, then try it out with your camera (use your camera manual to find the correct mode selections, etc.)
Look at the topics under Photographic Concepts to get an understanding of the relationship between shutter speed, aperture, and film speed (ISO).