A ceiling fan unbalanced will shake and bracing it usually isn’t an option. Correcting the ceiling fan wobbles will save wear and tear on the motor, quiet things down and improve airflow.
Start by cleaning the blades while being mindful of any fan weights attached to the blades. If there are weights attached to the blades you may want to mark the spots and remove the weights so if you have to balance the fan you will be working with a clean slate. While you are at it, inspect the blades for damage in case someone got a ladder or pole into the fan blades while it was running. Damage to a blade may have bent the bracket that attaches it to the motor causing a fan to wobble and shake as if it were out of balance. Then check the blades and blade brackets for loose screws.
If everything is tight, set a stepladder at the outer edge of the blades. Be sure it is stable and get your head high enough so you can look down one blade and sight across to the opposite blade. If they appear to be straight rotate the blade and sight the next set of blades. Do this until you are sure none of the blades are bent up or down compared to the other blades.
If all is tight and looking straight, you will need to balance your fan. Fan balancing kits are sold at hardware and lighting stores. Usually they come with a clip you can change from blade to blade and some weights.
Mark a blade and attach the weight to the blade midway from the motor to the tip. Run the fan slow at first gradually increasing the speed watching for improvement. If the wobble increases stop the fan and try the next blade working your way around the fan. Once you find the blade that shows the most improvement with the clip, try moving the clip closer and further from the motor for improved results.
Once the fan is balanced, replace the clip with a weight and move the clip to other blades for improved results if needed.
For more satisfaction with a reversible fan, have it blow down in the summer and up in the winter.