See the difference in high vs low ISO settings
Higher ISO settings will let you use faster shutter speeds, but at a price
ISO200, 1/4 sec
This gives the best quality because the camera is working at its minimum ISO setting, but the shutter speed is so slow that it will almost certainly cause camera shake if you attempt to shoot with the camera handheld.
ISO800, 1/15 sec
ISO800 used to be considered very 'fast', but today's DSLRs produce good quality even at this setting. You will notice more noise, but the shutter speed is 1/15 sec, which is still marginal but more likely to give a sharp picture.
ISO3200, 1/60 sec
Increasing the ISO to 3200 gives much more noise, but it's still not too obtrusive at normal viewing distances and it allows a shutter speed that should eliminate any camera shake, especially if your lens has VR built in.
ISO12800, 1/250 sec
At this ISO setting, the picture quality is relatively poor, so you probably want to avoid setting the ISO this high if you possibly can - but it does allow a shutter speed of 1/250 sec, which would freeze most moving subjects.
How much noise is too much?
It's easy to zoom in on an image on the computer at 100% magnification and see every dot and speckle of noise. But don't forget that this is a very high level of magnification, especially if you're using a camera with a larger, higher-resolution sensor.
The danger is that you can end up paying far too much attention to areas that are too small to see at normal viewing sizes and distances.
Night photography: how to set up your camera to shoot anything
Black and white photography: what you need to know for perfect mono pictures
Master your camera's autofocus: which AF points to use (and when to use them)
What camera should I buy: pros and cons of each camera type