"Countersteering" may be what you're looking for here... First of all, NO BRAKES! As you approach the corner, "twitch" your handlebars to the opposite direction that you want to turn... for example, if you are going to turn right, twitch the bars slightly to the left, which causes your bike to lean to the right. As soon as you feel the bike start to lean, put your outside pedal all the way down with some weight on it to help you maintain traction, tuck your inside elbow in to make the bike carve into the turn, and look up and out at the line you want to follow. This last is important, since your bike is going to go where you're looking.

This works well on the road and dry trail, where you've got traction problems (wet leaves, mud, wet trail) you will likely want to bleed off a little speed before starting your turn. Just be sure to lay off the brakes while you're turning...