Here's your greenside sand lesson in two words: speed and bounce. Splashing a ball out of a bunker takes more power than you might think—that's the speed part. And to use that speed effectively, the club has to slide through the sand without getting stuck—that's the bounce. Focus on a few keys.
First, grip the handle more in your fingers than your palms. This will help you hinge your wrists on the backswing—notice I have a full wrist set by halfway back (above). I can use that lever to generate speed quickly.
Second, lower the handle at address, feeling more bend in your wrists. When your hands are low, the heel of the club is more exposed, and that helps the clubhead glide through at a consistent depth. Setting the hands higher raises the heel and can cause the toe to dig, which stops the swing short.
Third, stay centered as you go back, and then swing to the left through impact. To maintain the club's bounce, don't let the shaft rotate counterclockwise as you swing through. Your trail hand should stay under the shaft, the knuckles on your lead hand pointing up. Use these keys to hit quality bunker shots.