Aside from the obvious smudge on the lens, blur can be the result of poor focus or slow shutter speed.
If the problem is slow shutter speed, then you've got to increase your shutter speed. I'd like to clarify the point someone else made that if you're getting blur indoors you're not using a high enough ISO or not a large enough aperture. ISO and aperture are not the root cause of the problem but they are related. Shutter speed is the problem. However, increasing the shutter speed will result in underexposure (dark images), because less light is entering the camera, so you'd need to compensate by using either a higher ISO, using a wider aperture, adding light to the scene, or a combination of these three. Additionally, if the motion is caused by your hand-holding the camera, not subject motion (for example, if you're shooting a still life), then another solution is to stablize the camera by using a tripod or some other method.
Image noise increases at higher ISOs and it's more noticeable in dark areas of the image. If you use a high ISO, but the image is well exposed, the noise won't be as noticible as it would if you used a high ISO but the image was underexposed. However, even in a well exposed image, high ISO noise will be apparent in shadows and dark areas, like if a person is wearing a dark clothing.
If you want to learn more read "The BetterPhoto Guide to Digital Photography" by Jim Miotke (highly recommended) or "Understanding Exposure" by Bryan Peterson (good, but not as much info on digital photography as the other book).
