Whether you are riding a rigid bike or a full suspension, the best suspension you have is your arms and legs. Stand up, relax and allow them to absorb the bumps and ruts on the trail. Once you learn to let the bike move beneath you, you will be able to float over most obstacles.
It also helps to relax your grip a bit on the handlebars. Be sure to hang on firmly but not too tightly. A white-knuckle death grip will cause your forearms and hands to fatigue sooner and then make it tougher to be in control.
Cadence, or the rotation of your cranks, is a very important aspect of cycling. Professional cyclists spend a lot of time developing a good spin. If you pedal in squares, or with jerky downward strokes, you are actually throwing yourself off balance and working harder. Spinning is not only more efficient, but it helps keep traction on loose trail conditions.
Good cadence incorporates pedaling in circles and being in the right gear. If you are geared too high, it will be difficult to power over things, and if you are geared too low, you’ll spin out and jerk the bike around. But if you change gears to keep the same pedaling RPMs, around 70 to 100, you’ll find that it is much easier to climb and pedal through rough sections.