Working on my action shots

I bought this new camera in the beginning of summer - it is a Nikon D60 SLR. No more lag time between pressing the button and the actual shutter being released. Plus I wanted to have crisper, clearer photos and be able to change lenses. I have all that and then some... but I need to work on my action shots. I was out in the yard yesterday and took a few of the dog running around. A little blurry and I think I figured out the problem - of course after the fact.

I think one problem is not shooting in the correct mode. The other problem is I move, too,
when in fact, I should stand still and let the subject move.

I have a dog show and then another dog event coming up in the near future that I want to make sure I get really great action shots from. I guess practice and more practice is what I need for now.