Vacuum away any surface dust and dirt with a soft brush attachment.
Clean dirt or hair out of small crevices with a toothbrush, tweezers or any pointed implement.
Mix a few squirts of mild soap with a gallon of water to make a soapy solution. If there is any mold or mildew on the furniture, add in 1/2 cup of bleach. Dip a sponge in the solution and use it to clean stubborn grime and stains. Avoid scrubbing too hard.
Rinse the furniture with a garden hose and allow it to air dry for 24 to 48 hours. Avoid leaving it out in direct sunlight. Hot sun can dry out vintage rattan and weaken the furniture.
Strip the furniture with a furniture stripper if desired, following the manufacturer's directions. In general, allow the stripper to work long enough to be able to use a brush to push off the old finish. Tilt the furniture as necessary to prevent the stripper or old paint from pooling in the crevices.
Spray the furniture with primer, allow it to dry and then paint as desired. Antique rattan can be painted with either oil or latex paint. Alternatively, the furniture can be coated with a clear finish.