dan - in layman terms. put it on aperture priority and turn the dial so it's maxed out. choose the highest ISO you can so that it isnt noisy (each camera has different noise levels but as a rule of thumb anything over 400 on a Point and Shoot camera is shit and over 800 on a DSLR is risky).

if you've done that, and it's still blurry whilst trying to hold it as steady as u can, then get a better camera and/or lens.

and one other thing, the more tele u use on your zoom, the faster u need to shoot to stop blur.