When you are just starting to try to ski well in moguls, start on small bumps in not too steep terrain. Moguls on Black Diamond trails can be both intimidating and dangerous to beginning mogul skiers. Many ski resorts have begun to set aside small "chutes" of seeded (man-made) moguls on Blue Square slopes just for practicing. Seeding just the sides of steeper trails, so skiers can practice and still be able to ski out of the bumps in case of a misstep, has also become popular.
Use the Mogul
Don't always try to zip through the troughs or go around the bumps, especially early on in mogul skiing. When you ski up onto a bump or ridge use the top, when your tips and tails are not touching snow, to change direction or initiate an edging down the front side for speed control.
Don't get into the habit of looking down at the mogul immediately in front of you. When your head is down, you are already out of balance and moguls come at you much to fast to not look ahead and pick a route or line. Even if you have to change your line, keep looking down the hill, and remember you don't drive a car by looking at the hood.
Absorb the Bumps with Your Legs
When you ride over a bump, use your legs like a shock absorber. Rising on the mogul, flex your ankles and knees to keep from being launched off the mogul. Then extend into a tall stance on the back side, and use the extension to turn or check edges as you ride into the trough.
Keep Your Poles In Front
Get in the habit of keeping your poles within your vision and moving with your turns. This aids balance and rhythm, and keeps you from falling into the backseat (the backseat is when your body mass is no longer centered over your boots, but falls back behind your boots and bindings).
Side Slip for Control
Speed control is the most important factor in mogul skiing and side slips and hockey stops come in quite handy in the beginning. They can evolve later into a nice flat ski and edge feathering technique.
Help Your Head
If you have a helmet, wear it in the moguls and keep your speed to your comfort level. All those great mogul skiers you see on the slopes have one thing in common - they all try to stay in their comfort zone.