There are programs out there that will clean up digital noise. I've always heard great things about Noiseware and Noise Ninja. There are free trial versions of other programs out there, but they're worthless. Break down and spend the money on one of the two programs I mentioned above.
When shooting at night, I always try to bring my 50mm 1.8 with me. It allows me to shoot at a lesser ISO while keeping the aperture wide open and the shutter speed in the medium fast range. Really try to shoot at the lowest ISO at all times. If you're shooting at night and you're shooting people who are moving around and you don't have a lens that will allow a large aperture, then to get the shot you will have to sacrifice for the high level of noise by using a high ISO.
If shooting during the day. Just turn the ISO down to 100-200 and the noise will go away.
Digital Noise does really depend on when you are shooting, your lens, iso and ss. Can you give more info on when you are shooting and what settings?
As for removing noise, I agree with Jon - I use Noise Ninja but be wary that sometimes it causes the photo to look really fake if you over do it.