It's worth knowing what the stone is made of, because you can expect different performance from different types, and the use may be different, in particular the appropriate cutting lubricant.
I'm not sure I would use any stone dry, although diamond plates (not stones technically) might be best used dry for some applications.
An old whetstone is probably natural (hard or soft Arkansas), aluminum oxide, or silicon carbide. All these will work well, perhaps best, with a honing oil which is just mineral oil, available from any drugstore (laxatives aisle). That's what the more expensive cans labeled "Honing Oil" will contain.
A waterstone is something different and I won't describe it here except to make the perhaps obvious observation that they are lubricated by water rather than oil. In both cases, the lubricant floats away the cutting swarf so it doesn't load the abrasive surface and diminish the stone's cutting capacity.
An oil stone, whether natural or synthetic, can be cleaned in an ultrasonic cleaner if clean is what you're after. While it will improve the appearance, perhaps greatly, it doesn't by itself address other important conditions such as flatness and fresh, sharp grit on the surface. For that you need lapping.
Lapping is essentially grinding the grinding stone itself. This can be done using a diamond lap like this:
although these are a bit expensive if you're not going to make frequent use of it. There are other alternatives to be found if you search a bit.
Armed with a lapping plate and ultrasonic cleaner, a set of oil stones will literally last a lifetime. I can't say I'd recommend such a setup to most folks, because they wouldn't use it enough to justify its cost. I happen to use stones frequently for various metalworking purposes so it's a worthwhile investment to me and I already have an ultrasonic cleaner for many other purposes.
Even without lapping, a clean stone will likely cut better, and a certain amount of grit renewal can be had by rubbing two bench stones together. Of course you have to have two :)
One last remark, going back to the type, if it's a hard Arkansas stone it is a great stone, probably the most expensive kind out there, but will sharpen frustratingly slowly. That type is more for refining and polishing an edge that's already been sharpened by a coarser stone.
If it's gray, the stone is probably silicon carbide. If it's orange, it probably aluminum oxide. Silicon carbide cuts faster, but wears more quickly so is harder to keep flat. Aluminum oxide is probably the best all-around choice for starters.
