Turn off the ceiling fan. Place a drop cloth underneath it. Put on goggles or some other type of eye protection. Next, clean the dust and dirt off the fan blades, using a ceiling fan duster. This will aid in balancing the fan, as dust accumulation is generally not even on all the blades. This slight weight imbalance contributes to wobble. Clean your fan on a regular basis.
Place a stool or ladder off-center from the ceiling fan. Unfasten the blades with a screwdriver, and turn on the fan. If it still wobbles, unfasten the mounting assembly that holds the motor to the ceiling, using a screwdriver. Ask someone to assist you by holding the fan motor while you're fixing the rocking.
Tighten the retaining bolts on the mounting bracket, using a pair of pliers or a wrench. Reconnect the fan motor to the mounting bracket tightly. Turn on the fan; it should no longer rock or sway. Turn the fan off again.
Fasten the blades to the motor with a screwdriver. Turn the fan on. If the blades begin to rock or wobble again, one of the blades is unbalanced. Open the fan balancing kit. Take the clip-on blade weights out. The clip-on weights are "test" weights to help you find which blade is out of balance and at what point on the blade.
Clip the weights onto the fan blades, following the manufacturer's instructions. This may take several attempts before you find the right position. Once you've found the correct spot, wipe down the blade with a damp cloth. Dry it with another cloth and stick the adhesive weights to the fan blades at the proper location.