I put cornering in the advanced skills section, because we will focus on the intricacies of the different types of conering and it won't do you any good keeping so many things in mind while fighting to stay upright.
There are several types of cornering:
The basics are the same, in all these cornering scenarios:
Up to say 80 degrees, when you don't need any special traction management, you should be standing throughout the corner. This is the most useful type of cornering in the woods.
Cornering is initiated by countersteering, leaning with the body and weighing the inside peg. Weight can shift back to neutral or outside, in mid-corner.
Lean the bike into the turn, keeping your body upright, unless it's a banked corner like a berm, where you keep your body inline with the bike.
In a slow, tight corner, you will slip the clutch and stay on the rear brake a bit, to keep the bike going slowly. To corner, you lean the bike inside and move your body outside to balance it out.
Here's the basic motocross cornering technique (whipping the bike around a tight corner):
Here's some videos and photos on cornering: