Determine the source of the shaking. Oftentimes, one leg of the folding table is uneven with the other legs, causing the table to shake. Sometimes this is no fault of the table, but of the floor upon which it sits. If the floor is uneven, then the folding table will not sit evenly.
Cut a piece of cardboard approximately 1/2 to 1 inch wide and 1/2 to 1 inch long with a pair of scissors. Make sure that the piece of cardboard is big enough to fit beneath the leg of the shaking folding table, but not so big that it is noticeable.
Lift up the leg of the table that is the source of the problem and slip the piece of cardboard beneath it. Test the table for stabilization. If it still shakes, repeat the above process on another leg if necessary. If the same leg is still the source of the problem, slip more cardboard beneath the same leg to thicken the cardboard until the leg stabilizes.