Clean the teak furniture with water and mild dishwashing soap. Dip a sponge into the soapy mixture and scrub the furniture to remove all traces of dirt and grime.
Sand the furniture with medium grit sandpaper. Attach the sandpaper to a handheld sander, or palm sander. A palm sander will make the sanding job much quicker and will create a smoother finish. Sand the entire piece of furniture with medium grit sandpaper. You will know you are done sanding when the rich caramel color is returned to the furniture and all traces of weathered gray are gone.
Switch to fine grit sandpaper. Sand the furniture to smooth out any imperfections. Wipe away all sanding dust with a damp rag.
Apply shellac to the teak furniture with a paintbrush. Apply the shellac quickly. Work from the top of the furniture downward. Avoid painting over the same area multiple times. You can touch up any missed areas on the second coat. Allow the first coat to dry.
Apply a second coat of shellac using the same methods used to apply the first. Continue applying coats of shellac until the furniture is completely coated. Allow the second coat to dry.
Rub beeswax onto the furniture to protect its luster. Rub the wax on with a rag. Buff with a different, clean rag to remove the excess wax and polish the furniture to a shine.