The best way to see if a stain is oil-based or water-based is to take a cotton ball with rubbing alcohol on it, wipe it along the woodwork, and let it dry. If the stain lightens, then it is water-based.
It is important to know if the stain finish on the furniture is oil or water, as each has its own methods of removal. Another way to determine the kind of stain is to take some water and sprinkle it onto the stained surface. If it beads up, the stain is likely oil-based. This does not work, however, if there was a polyurethane or lacquer applied over it.