This position will help you gain traction while keeping low and stable. Stay over the top of your bike, and drive the edges of your tires into the terrain to carve the corner.
Head - Once in the corner, look through and past the exit.
Hands - Push your inside hand towards the floor.
Hips - Twist your hips so they are facing the exit and keep them low.
Bodyweight - If you feel your tires lose traction at any point, move your weight backwards or forwards to aid grip.
Feet - Bend your knees and direct your bodyweight through your outside pedal.
Bike - Lean your bike over to drive the edges of the tires into the terrain.
Line - Enter wide and aim to hit the apex of the corner late to straighten out. On flat this is generally the best way to get around corners fast.
Tip: Get low - low is stable, and the lower you can get on your bike, the better you'll corner.