Flip the table over, and remove any feet covering the bottoms of the legs.
Drill out the centers of the ends of the legs of the table to create hollow hiding spaces. Do not remove more than half of the diameter of the legs. The compartment sizes will be limited and depend on the thickness of the material used to construct the legs.
Use a razor blade to shave pieces of cork to fit each hole. Insert your items, insert the cork as a stopper and replace the foot on each leg.
Invert the table and inspect the construction. If it involves a braced wood frame, cut a piece of wood to run parallel to and in front of the original corner brace. You may need a miter box to achieve the proper angle. Attach the second brace piece to the frame.
Cut a thin piece of wood, 1/4- to 1/8-inch-thick, to fit atop both braces, acting as a lid and creating a small compartment.
After placing your items inside, nail the wood into place to render the construction permanent looking. For a compartment you can open and close often, install hinges between the inside of the lid and the added brace piece. Because the lid to the compartment is thin, you can glue the hinges to the wood, rather than using screws, as a shortcut. Otherwise, screw the hinges in place.
Drill a small hole in the center of the lid, on the side opposite the hinges. Tack a small nail to the back side of the original brace. Run 1 1/2 inches of a length of wire through the hole, then twist the end of the wire around itself, leaving the remaining length free. Draw the wire tight and wrap the free end around the nail to hold the compartment closed.