Start small (duh!)
First find a moderate slope. Stand with your poles in the snow, facing down the fall line. Lift your poles up so you start sliding then you simply tip onto your edges and the turn happens. I don't know what people call this drill, but it is basically going from fall line into the bottom half of a turn. This action is the same thing you will do when you land your cornice drop: skis on snow, pointing down the fall line and immediately turn to a stop.
Your first cornice drop should be from a stop and on a pitch that is not more than 45 degrees or has an extended run out. Both criterion are selected to reduce anxiety. You should feel comfortable on the terrain.
Stand at the edge of a road or small cornice, square to the cornice line, with your tips over the edge, almost up to the binding. Relax. Gently push yourself over the edge but decisively and immediately bring your hands forward in front of you with your arms relaxed, but extended. You want to tip over the edge so that your skis become parallel to the snow below. As soon as you contact the snow, initiate a turn one way or the other and either stop or continue with more turns.
Dropping a cornice is easier if you are perpendicular to the edge as you don't have to deal with one ski leaving the snow before the other; they leave the snow simultaneously. Don't start with any speed, just let the skis tip over the edge. Allow your skis to match the angle of the snow while you move your hands and upper body forward so that when you are on the pitch below the edge your body is essentially perpendicular to the snow and your skis parallel to it.
Once you are comfortable with the move of pressing forward with your hands and letting your skis go from matching the angle of the take off point to tipping them (along with your body) to match the landing zone, you can start adding a little speed. Not much. You need to learn how much speed will get you in the air without sending you too far down the slope.
Don't, repeat DON'T, add upward energy (jump) off launching point. Just let the skis slide and press your hand forward, letting your hands and arms pull your body forward so that when you land your body is perpendicular to the snow and your skis are parallel to the snow.
@James shows nice form here, illustrating much of what Dean mentions above in his bullet points:
Hands forward
Looking at the landing
Flexed legs
Skis parallel to landing zone
Body perpendicular to skis and landing zone
Just so you know, I don't teach this kind of stuff; I'm just writing what goes through my mind when I'm going to drop a cornice. The most important takeaway from this is that you don't need to come in hot to a cornice to get air. The steeper and longer the drop off the less speed you need to get good air. When I'm going into Zuma from Zuma Cornice, I don't have any speed at all because the area I'm landing in is very steep and I don't want too much speed before I start making my turns. For me, dropping a cornice is a means to access terrain, not the whole objective. I want to land and ski.
