Use a chemical stripper to remove the existing finish from the table. Use the directions on the product for proper application and use. After the stripping is complete, use medium grit sandpaper to sand the entire surface of the table. Wipe it down with a damp cloth when you are done to remove any dust.
Paint your table with a base color using a paintbrush; this will be the color that is seen through the sponging. Allow the paint to dry completely. Depending on the color you choose, you may need several coats of paint.
Squeeze the chosen color of sponging paint onto a disposable paper plate.
Moisten a sponge and wring it out to remove as much water as possible; it only needs to be pliable, not soaked. Dip the sponge into the paint and blot it on a piece of cardboard. For the sponge, you can use a synthetic sponge, but these have a more uniform pattern. Sea sponges are a better choice for a more unique look.
Apply the paint covered sponge to your table's surface in a tapping motion. Twist and turn the sponge as you work to give a non-uniform look to your table. Keeping your sponge in one position can lead to a repetitive pattern. For a more varied look, switch sponges periodically, since each sponge will have a different pattern.
Add a second color of paint using a new sponge in the same manner as the prior step, while the first color is still wet. Twist and turn the sponge as you go. This will mix the two colors of paint and give it more depth. If you want a more subtle, muted look, dab the paint with a lambskin cloth.
Allow the paint to dry completely. Seal the table with an acrylic sealer if you want a glossy look; or leave it unsealed for a more natural look.