Barri, you have a vaneer piece of furniture, it looks like from the pictures. Vaneering is an old, tried and true, if done well, process that imvolves gluing a thin layer of expensive wood over a less expensive wood substrate. Among many other types of wood pieces that typically vaneered are sewing machine cabinets. Other items are such things as dining tables because wood that is just not available or stable enough to use in full sections is available in the thin vaneer sheets.
It looks to me like you have an oiled finish. To test this, put a few drops of boiled linseed oil on a couple of places and try to rub it in. If the oil is absorbed by the oil, then you have an oil finish. If the oil is not absorbed, it's a film finish and you have to do further testing to see what the finish is. Teak is a naturally oily wood and therefore oil finishes are common on teak. (Teak oil is more of a marketing gimmick than anything really having to do with teak.)
Before you start with the Formby's, which is not a bad product, you might want to do a little reading. Understanding Wood Finishing, by Bob Flexner, is simply the best resource on both finishes and taking care of furniture. It sould be available at most libraries if you don't want to buy it. I don't have any financial interest in it, but it has more down-to-earth information than any one book should be allowed to have.
Barri, you have what should be a pretty valuable table. The vaneer looks like it's it decent shape. Repairing vaneer is usually a job for a pro--and that's not my business either. If you do try to do-it-yourself, remember that there are 2 thickness standards for vaneer. My guess is that this piece came from about the time of transition from the thicker to the thinner. No guess on what your's is. The thick is a lot harder to find, but is available.