Carving 101

I found a nice, newly paved road with a gradual slope that I can practice my turns on, and guess what? ... I finally got it! The trick is going fast enough so that you can turn by opening your shoulders into the direction you want to go and leaning into the turn a little. Here's what I mean: If my left shoulder is pointing down hill and I want to turn to the left, I would open my chest by pulling my left shoulder back, and then lean backwards a little. To carve to the right I would pull my right shoulder back and rotate the upper body so that my left shoulder is actually leading the turn, then I'd lean forward.
Basically the same technique for turning is applied when riding horses. You look where you want to go, which turns your shoulders, which turns your hips, etc. I think the saying to remember turning sequences in Pat Parelli's Natural horsemanship is "eyes, bellybutton, leg, reins." You can visualize how this would work with longboarding, and skating too.