Since the first day new skiers click into their ski bindings, their quest is to learn how to parallel ski. Watching an expert skier float through acres of untracked powder snow is everyone's dream, and to realize it you must learn how to parallel ski.
Parallel skiing is actually easier than skiing in a wedge or snowplow because both skis are doing the same thing. When one ski tips to the right, the other ski also tips to the right, and vice versa. Of course you do have to develop the proper skills.
Pick a beginner slope with few skiers and stand with your skis across the slope, about a 10-to-15-degree angle across the slope. Place your weight equally on both skis, with your weight equally distributed between your toes and your heels. Your boots should be directly under your hips with plenty of room between them. As you push off, press forward with your shins against your boot tongues on the front of your boots. At the same time, gently tip your knees uphill. Imagine turning a radio volume knob to the right to increase the volume. Tipping your boots uphill engages the edges and turns your skis uphill.
Turn around and repeat the same process in the other direction. Don't be surprised if it's easier in one direction than the other, since one leg is often stronger, and skiers are more comfortable when the stronger leg is downhill.
After successfully repeating the drill in both directions, try pointing the ski tips downhill a little more each time, until you can complete a parallel turn by starting with your skis pointing almost straight downhill. Repeat in both directions.
Now try linking a right-hand turn with a left-hand turn. After turning left, center your knees, let the ski tips swing back to the right, and as they start to point straight downhill push your knees to the right, driving the skis into the turn. As you turn right, center your knees, let your skis swing back to the left, and as they point downhill push your knees to the left, driving your skis into the turn. Voila! Linked parallel turns.