What kind of finish is on the wood now? If it is an oil-finish, about the only thing you can do is light sanding (with the grain) to get below any stain that may have been used. If it is a urethane (or a polyurethane finish)or a laquer finish, I would start with CitriStrip. It is an orange scented gel about the consistency of pudding, though they also make a spray (that I have never used, so can't say too much about it), that is biodegradeable, isn't particularly obnoxious if used indoors (smell wise), and is much more gentle on your hide. Still want to put some drop cloth down if working on any surface that might stain or be damaged.
If you brush it on, let it sit for 30 to 45 minutes, it should soften things up enough to use a plastic scraper type putty knife on to remove the bulk of the finish. A second application usually gets the remainder. Follow up with a wipe down with a soft cloth dampened with odorless mineral spirits to clean things up and see if there is any that has been missed. Word of warning, if you leave CitriStrip on for more than 1-1/2 to 2 hours, it will dry to a hazy glaze, along with the softened finish. If this happens, simply apply another layer of the gel to re-soften the previous application, let it sit for about 30 minutes and have another go at it.
After stripping it down, another wipe down with mineral spirits, then follow up with some light sanding. Then re-finish as you would other stocks - - sand as needed, damp wipe down and whisker, oil, oil, oil, oil, oil (or whatever finish you prefer)... followed with a coat or two of filler/sealer, then more oil, oil, oil, etc. Top it all off with some hardwood floor paste wax for a nice, smooth, hand-rubbed or satin finish.