If you're getting noisy photos (noise being the digital equivalent of film grain), then chances are that the camera has got little choice but to go to the higher ISO mode, which is will usually do as a last resort in most modes.
Yes, the trick is to reduce the ISO, but when you do that, you need to make up for the that by letting in more light in another way - chances are that the aperture is also maxed, so you're probably stuck with a slower shutter speed or using the flash. In circumstances where a flash is useless (too far away) or inappopriate (on rides, etc), you're stuck with a slower shutter, and if you're moving or you're taking pictures of something that's moving (like SpectroMagic), then you really have no choice but to use the higher ISO levels.
In that case, you can reduce the noise using post-processing software like Noise Ninja or Noiseware, however this also removed detail and gives a "plastic" look to the photo, but it's usually still better than the noise.
