My summary of what's been said so far altered to include tuck turns for getting beginners started, with an emphasis on angulating from the hips.
Instructors mentioned the following things helped adults learn to carve arc-t-arc their first turns.
1. Some instructors start the teaching with tipping both feet/legs/skis, both the same amount and at the same time... without rotating the skis across the snow, and without using the hips. That "without rotating" part is a big deal. W-a-i-t-i-n-g for the skis to turn is a challenge; it calls for patience and allowing the skis to do the work. Also, skiers must recognize that tipping can be done without rotating. Static practice is necessary. A few instructors said that getting the skier to start the tipping with the ankles inside the boots is important; others mentioned tipping from the lower leg. IOW, teaching students to do RR Tracks is the initial goal that leads to full-on carving.
2. One (or two, did I miss someone?) instructors prefer to start the teaching with skating downhill, cleanly edging the propelling ski without any rotation. This makes the new outside foot/ski/leg in charge of the initiation.
3. Two instructors (I think) try to eliminate the persistent habitual rotation, which destroys the carving, by doing one-footed drills of some sort. This may involve picking up one foot/ski (either one) off the snow, or skiing in a wedge with the inside ski flat while the outside ski is edged to make the turn without being rotated. One instructor (me) mentioned using a very wide stance to kill the rotation.
4. Two instructors (I think) attempt to get the skiers to progressively reduce the rotation to zero, rather than working with them to go cold turkey from the start. The rest seem to aim for eliminating the rotation altogether from the get-go.
5. A number of instructors mentioned they start students on beginner terrain in a straight run. The reason is that having tails following tips generates unexpected and significant speed.
6. Only a few said they start the process with students doing a traverse.
7. One or two instructors mentioned teaching adults to use a pedaling motion when beginning to learn to carve.
8. Two instructors mentioned using Deb Armstrong's poles/hands on knees to diagnose clean tipping.
9. Two (I think) mentioned the Schlopy drill, which encourages counter and angulation.
10. One instructor uses tuck turns with hip angulation, first low tucks then high, progressing to personal skiing.
Non-instructors mentioned that starting with the following things helped them learn to carve.
1. Beginning on gentle terrain helped several people.
2. Rolling ankles and shortening the inside leg helped a few people.
3. Two/three people mentioned counter/counter-balancing and angulation are a must-do for the ski tails to follow the tips
4. Two members mentioned that counting helps the skier to w-a-i-t for the skis to turn, to help with the patience needed to avoid turning the feet
5. One member mentioned that learning to not let tips drift at top half of turn and learning to not let tails drift in second half of turn (old school skis) was essential.
6. One member mentioned that learning what "critical edge angle" was and how to get it mattered.
7. One member mentioned that there are misconceptions about what carving is; some people think they are carving when they aren't. Implication: this fact might impact what's posted in this thread.
8. One member mentioned that inside leg management is a topic for advancing a skier's carving skills; must get it shorter and out of the way