Give yourself plenty of room to practice and flat ground to stand on. You do not want to lose balance or kick something over by accident.
Stand up straight, keep your feet at shoulder length apart and distribute your weight evenly. Your arms can be anywhere; but keep them to your side for this demonstration.
Take your left foot and slowly kick upwards and across your body. Reach the point where your leg is perpendicular from your body and even with your right hip.
Arc your leg back to the left side of your body. Have the highest point of the arc be the highest you can kick your leg. Keep your leg straight the entire time.
Stretch your left leg as far left as it will go before returning your leg to the initial position. Try and keep the arc of the kick as close to a circle as possible.
Try the same steps with your right foot. Start by kicking left, across the body, and then, in a big circular motion, kick left, away from your body, and return to the initial position.
Repeat the fan kick at different heights. See how high up you can fan kick, then try a few fan kicks low to the ground. The basic fan kick is about waist high, but jazz dance welcomes variations.
Try doing the fan kick and pivoting at the same time. Fan kick with your left foot, but instead of returning your leg to the initial position, kick your leg farther and end 90 degrees to the left.
Put on some upbeat jazz music. Start dancing to the music normally. Then, when you have the rhythm down, work in the fan kick wherever possible.