So you got the equipment*, you've found a groomed trail (gotta stay on top of the snow or it won't be fun), and you're ready fly down the trail. Excellent! There are many methods of learning skate-skiing. Here are two of my faves:
Shoot the Moon
Remember that "shoot the moon" game with the steel ball between two metal bars? Okay, I'm dating myself but here goes. Imagine your skis are the bars and your hips are the ball in the center. \ o / When you position your skis in a v-shape and lean forward (at the ankles), you'll naturally move forward. Keep leaning and you'll fall on your face...which is a great drill for young kids who love face plants! For the rest of us, catch yourself by throwing your weight onto one ski...and then the other...and then the other...and you're off!
Pizza - Penguin - Hip Push
In classic skiing, you keep your skis in a parallel, "french fry" position with the occasional "pizza" to snow plow or slow down. To start skate-skiing, put your skis in a reverse pizza position, with your ski tips outward and the body as the point. Now shift your weight left and right on your skis – like a penguin trying to stay warm. Now that you have the pizza and the penguin, all you need is a gentle push from your hips. Bend at your ankles and lean forward. Once you get that weight shifted just right, you'll start to glide on one ski then the other as you keep the penguin hopping left and right. The faster you go, the longer you can "ride the glide" on each ski before shifting your weight.
*Basically skis without fish scales or ridges on the bottom and poles that reach up to your chin.