Spinning is:
the easiest way to explain it is: spinning is pedalling with little resistance. If you feel resistance or even seem to be "pushing" against the pedals as you turn them - you're mashing your pedals. Think of the kids on the Big Wheels turning their feet reaaaaaaaaaaaaaaaaaaaaaaaaal fast - thats spinning.
The hardest thing for new people to understand (or even this old person!) is that you Can go Fast while spinning without pushing so hard against the gears. If visuals help, think of Lance when he rides, ever notice how fast he turns his legs without seeming to work so hard? That's spinning.
I found the best way for me to learn aside from the "one-legged spin" was to drop to a very low gear and pedal until I was bouncing on the saddle, then to up the gears 1 gear at a time while maintaining that fast spin until I wasn't bouncing anymore. (make sense?) You'll notice you'll be riding about the same speed or faster without tiring out your legs.
I've also noticed I coast a lot less when I'm spinning (unless I'm at the end of a century! ) coz I just don't need to "rest" my legs by coasting.
Life should NOT be a journey to the grave with the intention of arriving safely in an attractive and well preserved body, but rather to skid in sideways, champagne in one hand, strawberries in the other, body thoroughly used up, totally worn out and screaming: "Yeah Baby! What a Ride!"