Suzanne, it's pretty hard to see what you are seeing over the web but there is a good chance that it is a Tung oil or similar finish on it now. DO NOT SAND. Unless there is a shiny, glaze type look on the piece, just wipe it down with a solvent to get rid of the surface oil and dirt. Paint thinner will work, probably, but whatever you use, do it outside. The white water marks are just moisture combining with the surface oil, get below the surface oil and you will get rid of the white. After you are down to a good clean surface, then put on a new coat of oil. With a Tung oil finish, you should do this every year or so anyway. Follow manufacturers directions and be careful with the rags you use. They can spontaneously combust. Either leave them spread out outside for a couple of days or put them in a can of water.