Catching air on skis is super easy. Landing is slightly harder.
In any case, there are different flavors of 'catching air'. There is airing on a jump or other feature, then there is catching air when dropping a cliff. Some of the skills are the same, some are slightly different. When dropping a cliff, your skis leave the snow angled downward, and your trajectory is a fairly simple line from the lip of the cliff to the landing below. However, when catching air on a feature, your skis and body are oriented upwards, and in air you need to bring your skis and body into a downward orientation in order to land safely.
Some of the skills needed for either are the same. It is very important to remember that even though the point of the exercise is to catch air and get your skis off the snow, most of the work for a successful air is going to happen before you leave the lip of the cliff or feature, with the skis still on the snow. After your skis leave the snow, there is very little you can do to affect your body position, and nothing you can do to affect your trajectory.
Off of a drop, your number one goal is going to be to keep yourself centered over your skis at launch. Your natural inclination is going to be to get back on your skis, but you need to resist that in order to stay stable in the air and land successfully. Any safe cliff drop is going to have a steep landing. If it is a flat landing, walk away, because a flat landing is a hard landing, and inviting an injury. So you launch off of the lip, and you're going to accelerate very quickly, at 9.8 m/s*2, in fact. That means you're going to be going fast when you land, and since the landing should be steep, you're going to continue to accelerate on landing. 35+mph is something you should expect, so if you're back on your skis, its going to be a very hard job to keep yourself upright on landing.
Off of a feature like a jump, the dynamics are a little different. Being able to judge speed entering a jump is important, because you're going to want to clear the feature and not overshoot or come up short (called 'casing'). On launch, you are going to want to 'pop' with your legs. The most important thing when airing a feature is how you leave the lip. You want to make a significant move forward on your skis as you leave the lip. This will bring your center of mass forward faster than your skis, which will change the attitude of your skis to pointing down and ready for the landing. If you are in any way on the back of your skis when you launch a feature, you will be thrown backwards and likely end up with your skis higher than your head, which is a bad way to land.
The wrong way to launch a feature- Notice how far back he is. http://youtu.be/oyp_30-koec
The right way to launch a feature-http://youtu.be/A0z8ysyWGFs
The right way to drop a cliff- http://youtu.be/eSSexj-ANSk
The wrong way to drop a cliff- http://youtu.be/XkKGXO3AmiY?t=38s
These are the things you should be keeping in mind as you're trampolining or airing on your feet.