Everyone has seen the comedy skits where someone takes a hand saw and cuts down one leg, then the next, and so on until the kitchen table becomes a low coffee table and still wobbles. There are better ways that will actually work and will stop the wobble without putting a book of matches under the table leg.
First determine if the problem is in the floor rather than the table. If there is a depression in the floor adjusting the table will restrict its use to that exact position on the floor you may be better off moving the table to a more level area. You may be able to avoid the depression by turning the table so that none of the legs actually sit in the low spot.
You’ve got the table where you want it, and it still wobbles. First understand that a three legged table can’t wobble, so you only need to adjust one leg. To determine which leg will depend on how the table is constructed. Most tables today disassemble for moving. The legs are held to the table by one or two bolts, with one end permanently attached to the leg and the other end protruding through a bracket on the table.
This type of construction will allow you to shim or adjust the legs to a small degree. Check the table with a bubble level to determine which leg is causing the problem. Remember it might not be the direction of the wobble, one of the other legs may be to long raising the other leg off the floor slightly. Once you’ve determined which leg is the culprit loosen the nuts holding the leg in place. Its easier to fix a short leg as you can fashion a shim of multiple layers of paper, thin card board, or even corrugated cardboard and place it between the table top and the top of the leg. Tighten the nuts locking the shim in place, test and readjust as necessary.
At your local home center you can buy small wooden shims that would make the job even easier. Loosen the nuts with the table up right start the wedge into the space mentioned above and tap it in lightly with a hammer until the wobble stops.
If your table does not have removable legs another option would be to glue a layer of felt material on the bottom of the short leg. If this doesn’t do the trick you may be forced to shortening the long leg which is raising the short ones off the floor causing the wobble. Forget the hand saw, you must remove material slowly. A hand wood file, or rasp is a better choice. Go slow, take only a little wood off then turn the table over and check your progress. Another option would be a hand held belt sander. Again go easy as these will take down the wood quite quickly as well.
With care and patience I’m sure you can get Grandma’s cherished oak table to sit solidly in its proper position as the crown jewel of your formal dining room.