I love to quote an old coach of mine (imagine Russian accent): "Most important part of jahmp is JAHMP"
True. But I'd almost now say that most important part of the jump is the landing. You hear more masturbatory commentary at competitions about jump landings than about any single other issue in figure skating. The figure skating world has gotten so obsessed with the so-called "clean landing" that they actually have changed the rules to parse out the turns by quarters, so that good strong jumps get credit, even if the landing is not quite "clean." Essentially, an attempted triple that is a little short will now get credit for the attempt, rather than a harsh downgrade to the double, because the skaters were starting to go for the GOE on the lesser jumps rather than risk the point loss associated with downgrades (think Lysacek and the infamously nonexistent quad).
The parts of a jump are the entry (lift off), the creation of rotation, air position, and landing. Interestingly, one of the first things you teach a beginning free style student is not the entry, but the landing, starting with the touch down and the check-out position. A classic landing touches down toe first on a straight leg, free leg in front and head turned towards the direction of rotation.
That's right-- you land on a straight leg, with your free leg in front. The misnamed "landing position"-- bent skating knee, free leg extended behind-- is actually the checkout. That's the position you hit to stop the rotation as you glide out of the jump. If you don't land correct position, you'll pitch forward, digging your toe pick across the ice, in a spray of snow, kicking out a big divot. Snowy landings are dramatic, but they indicate technical problems. A clean landing is not just full rotation. It's also a light, snow-free touch down with no rotation on the ice.
There are lots of drills to teach that moment, and here's a few:
Backward pumps to backwards outside edge glide: Strong pumps on a circle, then back outside edge glide on a straight leg, free foot in front, pull the leg through to a back extension while bending the skating knee. Arms are in an L (skating arm pointing into the circle, free arm in front) and head turned towards the center of the circle. You should be able to hold this without letting the edge get tighter for at least halfway around a hockey circle. I make my students do this in both directions, no matter which way they rotate.
Moving hops: Once a student has mastered the above, add 5 short hops to the final glide: just up and down from the landing foot, pushing off the toe. Bonus points for staying on the curve.
Stationary hops: Skater stands in a neutral position, arms and head in landing position, then balances on landing foot and does several small hops, first in actual landing pose (free foot in front), and then jumping up in landing position and doing landing-check (extended free foot behind). Again, both these exercises should be done by all students on both feet.
Rotating hops: Otherwise known as back scratch-loop. Student enters a back scratch spin from any entry- inside three or back pivot- and then does a serious of increasingly rotated hops while still rotating- half way, single loop, double loop. Arm position is optional: in checkout position, or pulled in tight.
There are also numerous moving exercises you can do using turns and both two-foot and one-foot jump combinations and sequences to help you feel the sensation of full rotation while moving at speed across the ice.