If you want to get faster, try to get hooked up with one of the reputable MX instuctors, they focus tons on corners, corners are where races are won or lost, everybody can jump, albeit some better than others, not everybody can corner. The turn right to go left works on dry, hard, slick corners, doesn't work on a well prepped MX track. Kawi's are NOT great tight turners, but with the right set up they can be made to turn well.
As far as technique, you should be driving into a corner as Jeeks said with elbows up squeezing the tank and standing, when you start braking you should be heavily on the front brake (the rear isn't doing much) as you start into the corner you should transition your body to a sitting position, if the corner is left handed your going to weight your right hand footpeg, you should have the gear selected that you will use coming out of the corner. the inside leg should be extended to try and load the front wheel, the corner will dictate when and how much throttle you can use and whether your going to use an inside line or outside line. during a practice session you should try to develop lines that may not be the preferred line, if your in a race and you have to pass somebody and they're in the preferred line you have to find some place to pass them, and if you have lines developed during practice you have a place to pass.
If there are ruts you can use your rear brake to hold you into it, just drag it a bit and you'll be suprised at how well it works.
