Stand with your heels together, toes slightly apart and knees slightly bent. Move one knee forward, then bring it back to the original position as you bring the other knee forward. Repeat slowly at first to get the rhythm, then gradually work faster. The movement of the knees is what gives the illusion of the hips moving. Let the heels and knees do the work and let the movement of the hips follow, but don't force the hips or waist to move.
Keep the shoulders still as you move your hips. You should not be able to tell the bottom half of your body is moving from looking at your upper body. The shoulders should be relaxed, but not stiff. Keep the arms gracefully extended, with the elbows and wrists slightly bent, not locked.
Try the slower movement of the hips. In addition to the quick hip-shaking movements, Tahitian dance features smooth, controlled hip moves. Stand in the position as you would for the fast moves. Pretend there is a pencil on your hip bone and that you are drawing a figure eight on the wall in front of you. The knees again are the main impetus for the movement, but you will feel your abdominals as well. Lift one heel, which will lift the hip, and bend the other knee a little lower, lowering the opposite hip at the same time. Make the moves as symmetrical as possible, so as one figure-eight ends, the one started by the other hip bone begins.
Add some costume elements. The aesthetics of the movement from the hips are enhanced by the distinctive traditional costumes of Tahitian dance. The "grass" skirts Tahitian dance performers wear are actually made of a special kind of tree bark found on the islands of French Polynesia. If you don't have access to this specialized costume, a sarong or large piece of fabric tied tight around the widest part of the hips and knotted on the side can accentuate your moves. Some dancers wear coconut bras, but a short top can suffice if you find this idea too uncomfortable for practice. The most important aspect of your clothing is comfort and the ability to see your torso.
Add levels. As you become more comfortable with these moves, you can do them with the knees more bent or on the toes. Try lowering yourself to a squat position as you move the hips, always remembering to keep the shoulders still and relaxed.