Over months of heavy use, screws in ceiling fans often loosen, causing the fan to shake. Tighten all screws at points where blades connect to the body and where the body connects to the ceiling. Run fan on high. If your fan still shakes, the problem is either a bent blade or a fan imbalance.
Warped blades also cause shaking. Position yourself at eye level with fan blades. Check blades against each other, two at a time to determine which blade is bent. Bend blades made of flexible material like pewter in the opposite direction of the warp until straight. Replace blades made of metal or wood. Check your box for extra blades before you purchase new ones. Fans that are still shaky after you adjust or change damaged blades, may have an imbalance problem.
Balance kits are often found in the fan's original box. Laundry pins and a 3/8 flat washer also work to balance fans. Clip a laundry pin at the middle of one blade and run fan to see if it is still wobbly. If the fan is stable, clean blade and tape washer in the center of the blade. If the ceiling fan is still shaky, repeat process until the appropriate blade is found.