Drop the outside pedal.
Dropping your outside pedal whilst cornering lowers your centre of mass and gives your tyres extra grip. The downside is reduced pedal clearance on the outside of the bike so make sure there is nothing it will catch on through the bend.
Lean the bike in the direction of the turn by extending your inside arm and pulling the outside grip towards the centre of your chest. Put all your weight on the outside pedal, boost the effect by pulling up on the outer grip as you turn and pushing down on the inner grip.
Whilst learning this new turning technique taking your inside foot off the pedal will give you extra confidence to push the limit of your grip on hard or slippy surfaces whilst making sure all your weight goes on the outer pedal. Pull up with your outer hand to apply even more pressure to the outer pedal.
Face into the corner.
Commit yourself to the turn by turning your hips, shoulders and head in the direction you wish to turn and look around and past the corner to make sure there are no surprises waiting. Move your hips over the outside of the bike to add extra weight onto the outer pedal and encourage the bike to lean further over.
Find the limits.
Keep trying the same corner faster and faster until the bike reaches the limit of it's grip then back it off a touch. Once you are confident turning at speed, keep your inside foot sat lightly on the pedal to get back on the gas quicker as you exit the turn.
If the the bike starts sliding, stay calm, the inside foot is your 'get out of jail free card'. If front of the bike starts sliding use your inside leg to shove yourself upright again whilst moving your weight forward on the bike to get more traction on the front end.
If the rear starts to go you can use your inside leg to push your weight back over the bike or, if feeling confident, try to ride it out foot up. Either way, adjust your steering towards the outer edge of the corner for a second or two which will help to bring either wheel back in line again before recommiting to the turn.
If the trail surface looks to be hard or loose, move your weight further forward than usual to get more grip on the front end as a rear wheel slide is much more predictable and easier to correct.
Look up the trail as you start to exit the corner, bring the bike back to the upright position by pulling up on the inside grip and moving your outside hand back to it's normal attack position. Start pedaling with your raised inside foot as you bring the bike upright whilst straightening your hips and shoulders in one smooth movement. It may be that the next corner goes the other way and all you need to do is swap the raised pedal over but by turning the cranks forward you get a firm pedal to help compose your balance a free pedalstroke to boot.
When changing from a corner in one direction to one going the other way try to make your change smooth rather than jerking the bike over. Use a forward pedal stroke on the inner raised pedal to unweight the bike as you come change direction. This will pop you out of the first corner a little quicker and help you flick the bike over ready for the next turn. As the bike weights up again the extra grip you get can be used to help you turn into the new bend.