I am not sure what kind of digital camera you have. However, my Canon S1IS shoots very grainy pictures when the light level is near the lower limit of F-stops it can pick up. On many models, the F-stop that is set by your auto exposure program is displayed when you look through the view finder. If you are seeing some really low numbers, and you are shooting with the built-in flash, you may well get a grainy picture. Try increasing the ambient light, or use an exernal flash - if your camera is fitted with a hot shoe for one.
Your camera settings might also be to blame. Most digital cameras have a white balance adjustment, and yours might be off. You would need to refer to the manual for your model to figure out how to set this. You may also have your camera set in a mode it doesnt belong in for the kind of picture you are trying to take. Does your camera have a