Most riders can rip toe-side turns, no problem: It's natural. You're facing the hill and you can see what's going on. When it comes to carving on the heel side, however, beginners tend to straighten their legs and the board bounces across the snow, half out of control.
Fixing this problem starts at the top of the turn. Using the momentum from your toe-side turn, roll your board onto the heel-side edge by lifting your toes inside your boots. At the same time, sink your butt into the hill, as if you're sitting in a chair (Fig. 1). Try to create a 90-degree angle in your legs, then drive your knees toward the tip as the board carves a clean arc (Fig. 2). The key is to trust your speed. It may feel like you're about to fall when you sit down, but the energy of the turn will keep you up. In fact, you have more power, not less, when you maintain this position, and you'll also have an easier time absorbing rough spots or recovering from a slide on slick snow.
Whether you're ripping around on a freestyle or a race board, sitting in the imaginary chair will help you rail that heel-side carve.