I'm not an amazing skier, but I feel like I have enough knowledge to give some light to 'how to cork'. There are two ways to cork when you really break it down. Hit the jump straight, or carve into it. These are written for a cork 7, the easiest cork to do, and what I think is actually easier than an upright 7 once you're comfortable with them.
Straight on - easier for learning:
-strong pop off the lip, just like with every trick.
-'drop' your inside shoulder to the spin while looking back towards the take off of the jump. Don't actually keep looking at the take off, 'cause if you do you'll stall out and just eat it. 'look' at the take off, but keep your vision going in that direction. I find grabbing tail helps with making sure the inside shoulder actually drops because your outside shoulder kinda goes up to grab tail if you look back at your take off, causing your inside shoulder to drop down. aka - commit!
- your landing will show up around that area. If you throw it too far down initially you'll spot your landing slightly higher than where you are looking, vice versa if you throw it more like a wobble than a true cork.
Carve in - feels way smoother:
(written for someone spinning left)
- come in wide on the skiers left side of the jump.
- before the tranny of the take off cross to the right side of the jump, aiming kinda near mid transition... but... don't come in too 'sharp' - you don't want too aggressive of a carve 'cause you want to keep your speed and have good control over the direction you take off during the carve.
- as you hit the transition start your carve, you should be near the right side of the jump when you hit the halfway mark up the tranny
-when you hit the lip you don't need to pop as much, just 'flow' off the jump keeping the lean of the carve going into your spin (aka - dropping the shoulder)
-because you aren't popping as much, and you can commit to dropping the shoulder I find it's easier to grab mute instead of tail and just hold until your landing comes around.
-the same as corking straight on, if you cork 'deep' your landing will be higher than where you're looking, and vice versa.
AND, I got way to carried away and involved with this post.