Spread tarp on the floor and place the wooden rocking chair directly on top of the tarp.
Pour ½ cup of Murphy's Oil Soap into the bucket of warm water, and place the bucket on the tarp to protect the floor from drips and spills.
Put on rubber gloves, and dip the sponge into the water. Squeeze out the excess soap and water to avoid drips. Using firm, even strokes, begin washing the rocking chair. Take care to wash in between all the slats, under the arms, the back, seat, and on and around the legs and rockers. For stains, finger prints, sticky spots and heavy dirt, use pressure. Continue this process until the chair is clean.
Dry the rocking chair throughly using your towel, making sure to get into all the corners, nooks and crannies.