First of all, all the noise produced from your camera is the ISO (ASA) sensitivity of the image sensor. That's it. Nothing else besides severe underexposure, a hot CCD or CMOS sensor, or a High ISO setting induces noise. It has nothing to do with your ability to keep the camera steady.
The thing about point-and-shoot'ers is that the image sensor on most are only about the size of a fingernail, as opposed the sensor on DSLR's that are usually a wee bit smaller than a slide of 35mm film. Because camera manufacturers try to pack a gazillion megapixels into such a tiny sensor, they produce an ungodly amount of noise in the image. That coupled with (usually) crappy lenses creates images that are noisy, off color, lack contrast, have color fringing, and lots of sun flare and glare.
Just for [snipped] and giggles, I uploaded a peice of a picture of my dog that I took on my D70. I cropped it alot becuase the orignal image is 3008x2000 pixels and nobody needs to see the entire shot. This crop is 854x837 so in comparison to the original shot, this it tiny. No photoshopping except for the compression and cropping was done. Because of the much larger sensor, and better glass, I could shoot at ISO 200 and have no noise whatsoever.
Shot with my D70 and 35-70mm lens at f/2.8 at 1/1000 of a second hand-held.
In comparison to Talldudes pic, the difference is night and day! BTW in actual prints, the difference between 5 and 6MP is completly unnoticeable.