If you've ever watched a good surfer in really bad conditions, you've probably been impressed with the speed they are able to make in what looks like mushy nothingness. These guys (and gals) have mastered the art of projecting out of their bottom turns and are using every little cup of a wave surface to bounce out of. If you learn how to load and unload your springs (legs) and push off of the bottom, you'll find your surfing improving significantly as you develop the ability to generate speed. And, as we all know, speed is life!
Want to see good projection? Check out Kelly Slater, look at the wave at about .49 and see how Slater zooms right by the guy ripping him off. The Snake muddles through a couple of turns, no projection. The 11x Champ, weighting and unweighting out of his turns, easily passes him by- lots of projection.
I'm assuming in this piece that you already know how to read a wave and make the decision to turn left or right on it. I'm also assuming that you've got the basics of actually redirecting the board figured out. I'm thinking that what you are looking for is a way to add some vitality to your riding- you want to go from slow cruiser to dynamic ripper, bouncing from section to section, carving with speed and flow. Sounds good right? Well, the key then is projection.
Basically, you are weighting (compressing as you drop in) and un-weighting (uncoiling off the bottom) the board through your bottom turn. If you've ever watched skaters or snowboarders in a half-pipe, you can see them doing the same thing; compacting their body as they drop down the half pipe then driving their legs and unweighting as they project up the opposite side.
A couple of tips. Turn your head and look to where you want to go, your body will go where the eyes are looking- so look far down the line and you will get there. Work on your timing. The better you get at synchronizing the driving pistons of your legs with the smooth lean and swoop of your bottom turn, the smoother the turn will look and the more projection you'll get out of the bottom turn.
And finally, if you're doing it right, your legs should be worn out at the end of a long ride. If they ain't burnin' chances are you're not projecting.