NOTE: I do not recommend getting on a ladder if you do not feel safe and comfortable in doing so
First, if the ceiling fan did work fine at one time but now it is shaking:
Loose blades on CEILING FANS can cause a problem.
Check for loose blades and loose connection between the rod and the fan body. If the blades are all tight, and the rod is tight at the ceiling fan body, check the mounting at the ceiling to make sure that it is secure. If this is OK and it is a four blade ceiling fan, then stand out away from the fan and point any one blade toward you. Look at the blade directly opposite it and see if they are basically in a straight line. If so, rotate the blades 90 degrees and do the same for the other two blades. If they line up, then you probably have a balance problem. If they don't, then you have a bent blade and this must be corrected before balancing. Usually after looking closely, you can tell which blade is bent and which way it needs to go back. Most ceiling fans have blade arms made of a pewter like material which will break easily when bent excessively. So be careful! If it brakes, then you need a new set of blade arms. If you have a five blade ceiling fan, then you must do your best to see if you can detect a blade out of place.
Once the blades are basically lined up, or you think they are OK then you can balance the ceiling fan. Balancing kits for ceiling fans are available at various stores. They consist of a clip and a number of weights that match the gram weight of the clip. But I prefer to use very high tech stuff. So go to the hardware store and get some 3/8 flat washers, a bag of clothes pins and a roll of 2" wide Scotch Mailing Tape. Both the kits and my high tech stuff work on the same principle but the kit usually only has one clip which is OK for slight wobble, but in my opinion, not for average or excessive wobble.
First, ceiling fans that are balanced while going in one direction, will usually be a little different when run in the opposite direction. When the ceiling fan turns counter clockwise, the high edge of each blade is catching air and the low edge is deflecting air. When reversed, it's just the opposite. The low edge now catches and the high edge deflects. So if one blade is a little higher or lower than the others, it will catch more air in one direction, but when reversed, the other three will catch more air than it does. If all the blades track the same, then after balancing, it will be the same in either direction.
Set the ceiling fan to blow down, (counter clockwise). Clip a CP (clothes pin) half way out on the lower edge of any blade. We will call this blade #1. If the wobble problem was real bad, clip two or three next to each other in this same location. Now run the fan at the highest speed possible. If the wobble starts getting real bad before reaching high speed, turn the ceiling fan off. Now move the clip or clips to the next blade, blade #2 and repeat the step. Do the same for each blade. Observe the amount of wobble as each blade is tried. You will notice that one way will be better than all the rest. On the top of this blade, you will tape a 3/8 flat washer approximately where the clip was. Note: The blade surface must be clean to the point where the tape will stick adequately. Otherwise you may sling a weight off while the ceiling fan is running and this can be dangerous. Test the surface by sticking a piece of tape to the area and see if it comes of. Now stick a piece, approx. 3" long, on the top of the blade in this area. Then using another 3" long piece, tape the washer down on top of the first piece. Note: you will use one washer for each clip that was on the blade. Run the ceiling fan. If still wobbling, put the clip back on the blade where you put the first weight, run and observe. Move the clip to the blade on the right of the weighted blade. Run and observe. Move the clip to the blade on the left of the weighted blade. Run and observe. One of these three will be better than the others. Put a weight on top of the blade at this point. Repeat process until the wobble is stopped. Normally 1-3 weights will be sufficient, but if real bad it may take 6-7. If the wobble gets worse with the CP than without it, then you have too much weight on already.