How to Carve on Snow Skis
To carve on snow skis, start by positioning your skis so they're shoulder-width apart. Then, as you're making a turn, apply pressure to the inner edge of your ski that's on the outside of the turn. At the same time, push your ski that's on the inside of the turn slightly forward. When you complete the turn, repeat the process going in the opposite direction. Keep turning and alternating directions as you make your way down the slope. At first, try to practice on gentle slopes, and then gradually work your way up to steeper slopes once you get the hang of it.
Start by finding a large, gently pitched slope, preferably with not too many people.  Practice making slow, parallel turns with your skis.  Position your skis a little more than shoulder's width apart. You don't want them so close that they could get tangled up with each other in mid-turn, but you want them far enough apart for stability. The right width is important in making banked turns without your knees colliding. Apply pressure to the forward-inside edge of the ski that will be the 'outside' ski for the turn (i.e. , right ski, if turning to left). Focus on putting you weight on the ball of your foot just behind your big toe and on your inside arch, at the same time as you press your shin forward gently on the cuff of the boot. As you start to turn, push your inside ski slightly forward (and lift that inside knee slightly, which will commit your weight to the inside of the turn) and let your hips fall in and forward toward the inside of the turn. Keep forward pressure on that forward inside edge of the outside ski until the turn comes all the way around. Make sure that no matter how sharp your turn is that your upper body remains parallel to the hill. (Not tipping your shoulders) Keep your forward and into-the-hill hip angle and stick with it throughout the turn. Commit to the turn! Do not exit the turn too early (which would be when you are accelerating straight downhill -- trust that your forward and inward pressure will bring that ski around). Remember: finish the turn skiing perpendicular to (across) the slope before going on to the next turn. Straighten your turning leg and step onto inside edge of the other ski at the same moment as you plant your pole for the next turn ("plant up", meaning plant pole as you straighten up and shift your weight). Then repeat, going the other direction into the next turn. Build a slight up-down rhythm that is also slightly rotary (forward-up at the beginning, or top, of the turn, on your big toe, and sinking to have weight slightly farther back onto your inside arch-heel as you come through the turn, to keep the edge from skidding, then up-forward again as you make your next pole plant.  At first, you can allow almost all your weight to be riding on the inside edge of your outside (or turning) ski. With shape skis, as you get more proficient, you can learn to keep more weight on your inside ski, carving that ski in the same fashion as the outside ski (except on the inside ski you have to weight the 'outside' of the ball of your foot inside the boot). 
Start by finding a large, gently pitched slope, preferably with not too many people. Practice making slow, parallel turns with your skis. Position your skis a little more than shoulder's width apart. Apply pressure to the forward-inside edge of the ski that will be the 'outside' ski for the turn (i.e. Keep your forward and into-the-hill hip angle and stick with it throughout the turn. Straighten your turning leg and step onto inside edge of the other ski at the same moment as you plant your pole for the next turn ("plant up", meaning plant pole as you straighten up and shift your weight). Build a slight up-down rhythm that is also slightly rotary (forward-up at the beginning, or top, of the turn, on your big toe, and sinking to have weight slightly farther back onto your inside arch-heel as you come through the turn, to keep the edge from skidding, then up-forward again as you make your next pole plant. At first, you can allow almost all your weight to be riding on the inside edge of your outside (or turning) ski. 