Great question, L2T. Beginning in the Half Pipe is a revelation for many people, but it is really pretty easy to do some basic moves. The pipe itself can be pretty intimidating at first, especially the big SuperPipes at some of the bigger ski areas. But you will get used to it quickly. Ironically, the biggest pipes are usually the easiest to play in, because they are well-maintained, the walls are vertical (non-vertical walls can launch you right out of the pipe), and the transitions at the bottom of the walls are smoother and more gradual.
First, you are absolutely right that, once you get high up on the vertical part of the wall, you can't just steer "regular" ski turns, and you certainly can't steer turns when you're in the air above the rim. The "weightless" turns that are basic to the Half Pipe break most of the rules of good steered turns. Whereas most modern skiing involves active feet and legs working beneath a stable, disciplined upper body, the basic Half Pipe move comes entirely from the upper body.
Think of it as a hop turn, in which you leap to become weightless while rotating your arms and/or torso to throw yourself into a spin once you leave the ground. Except it's easier than that in the Half Pipe--you're already going straight up, so you don't need to hop. Head straight up the wall. Just before you stall out, rotate your arms and torso slightly, to throw yourself into a nice 180 degree spin during the "weightless" phase. You do NOT need to clear the rim to do this, and I recommend that you develop the move lower down before attempting to clear the rim. You DO want to get at least to the vertical part of the wall, though, so that you are moving straight up. Be patient, wait until you feel almost weightless, then throw 'em around. It takes very little effort.
When you are ready to clear the rim, remember one very important thing: whatever you do to make the turn must happen when your skis are still in contact with the snow! In other words, the rotation of the upper body that throws you into the spin must happen while you're still on the snow. Once you're in the air, it is too late!
Pole plants are not forbidden in most Half Pipes, but they are discouraged (they damage the walls), and they are unnecessary. In fact, they can throw you off. If you learn to rely on a blocking pole plant to help your turns lower on the wall, you'll be in for a surprise once you're in the air above the rim!
Here are a couple thoughts for Half Pipe beginners:
Pay attention to the etiquette and safety rules of the park. Make sure others are aware that you are "dropping in."
Head straight up the wall! Conservative beginners are often reluctant to do this, because it can be intimidating, so they head up at about 45 degrees. But straight up is the most conservative direction, by far! If you angle downhill, you will not lose as much speed, and you'll gain a whole lot more speed as you come back down. Remember that the Pipe itself is on a hill, often fairly steep. If you head "downpipe," you will go FAST. So straight up, with a 180 degree turn back down and up the other side is the most cautious tactic. Head downpipe and gain speed only when you're ready!
Another common mistake is to make a big hop off the vertical part of the wall. As I described above, you don't need to hop, because you're already moving straight up. If you DO make a big hop, it will push you horizontally, away from the vertical wall, and you risk a big, hard fall into the bottom of the pipe.
Look straight up toward the rim as you approach the wall--not down at your ski tips, or at the middle of the wall. Looking up will help your body move as it needs to, more-or-less perpendicular to the snow surface all the way.
Have fun in the Half Pipe. It is a new environment for many of us (myself included), but it can be a lot of fun. Take it slow at first, and build as your confidence and skill develop. The suggestions I've given you above are mostly my own observations from playing a bit in the Pipe a little this year, and working with instructors who now have to do some basic Half Pipe moves to pass their Level 3 (Full) certification exams here in Colorado.