Not a "wet stone," but a "whet stone." To whet is to sharpen -- as in "whetting" ones appetite with an appetizer.
A stone with "two-sides" is called a "combination stone." Each side is a different grit -- one significantly coarser than the other. What the actual grits are, depends on the particular stone. There are three basic processes to sharpening -- profile/repair, sharpening itself, and polishing. Two surfaces can't do all three, so it helps to know the grit levels before jumping into any particular task.
Cabo has a lot of things right. One of them is that the first thing you have to do is determine whether the stone is a "waterstone," or an "oilstone." That's fairly easy to do, despite the fact that not all oilstones have ever been used with oil. Of course, most of them have been used with oil. The vast majority of whetstones to found in America are oilstones, not waterstones. So, you really shouldn't be too surprised if oil was used.
Soak the stone in water deep enough to cover it completely for about ten minutes, then start scrubbing it with a stiff brush. No soap, no detergent -- just the brush. If it's a waterstone, most of the dirt (actually "swarf") should start coming off. If it's an oilstone -- especially if it's been used with oil -- the brush won't make much of a dent in the grime.
Don't worry about getting water on an oilstone. Cabo was mistaken about that. It's absolutely not a problem. On the other hand oil on a waterstone can be quite a problem -- and you really shouldn't get soap on a waterstone either.
If it's a waterstone, there's not much need to clean it further. Normal flattening and use will keep it clean enough. The grime is a mix of dried out abrasive, binder and swarf called "slurry," aka "mud." Most waterstones work best with a bit of left over slurry. And once you do flatten and clean them, you have to work up some mud by sharpening or with a nagura stone to make waterstones work well.
If, as seems more likely, it's an oilstone, and it's as dirty as you described it's also probably clogged. Clogging means that the stones pores are full of swarf and gunk and that the stone can no longer cut metal cleanly. In turn, that means that stone will have to be thoroughly cleaned.
There are a number of ways to go about it, depending on how dirty the stone is. If the stone is really filthy, you'll have to soak it in a solvent like kerosene or mineral spirits, and do some sanding (you can use ordinary coarse sandpaper). However, as a preliminary let's start with something easier.
Try scurbbing the stone with an ordinary scouring powder like Comet or Ajax and a stiff brush. A wire brush like a barbecue brush is fine. Take your time and repeat the process a few times. After a while you should at least be able to see the actual colors of the stone.
If one side is orange-red, and the other grey-brown you have a Norton combination India -- and that's a good thing. The dark side is a coarse India and is useful for repairing knicks. The orange-red side is a fine India and is a very good stone for working up a sharp but coarse edge on soft steels. An 8 x 2 x 1 coarse/fine India runs just under $20.
If one side is light grey and the other is dark grey, it's probably a coarse/fine silicon carbide stone from one manufacturer or another (possibly a Norton Crystolon), and is most likely not worth saving. Not that the stones aren't useful, but they're not a first choice for kitchen knives (too coarse), and they're very cheap to replace. Nortons cost around $15, and everything else is cheaper.
If either of the surfaces is white or pinkish-white, chances are you have a combination Arkansas. Combination stones aren't expensive, but even combi Arkansas are still probably keepers.
After scrubbing and scouring the stone, the next step is to thoroughly wash it. The easiest way to do that is to run it in the dishwasher a few times. You CAN do this with dishes in the dishwasher -- no problem. But if you do, it's probably best to give it it's first ride when no woman is present in the house.
Another way, is to get some cheap chain and put it the bottom of a non-reactive pot to allow water to circulate beneath the stone, add some water, some dishwasher detergent (you want the dry stuff), the stone, and boil it for ten minutes. Turn the stone over and boil it for another time. The diswasher doesn't do quite as good a job, but it's easier.
If that doesn't get the stone really clean, you'll have to soak it in kerosene or some other solvent for a few days to loosen the dried up oil that's clogged the pores, thoroughly wash it (dishwasher), and sand it off. You can use regular 120# sandpaper if you like.
For the time being, there's no need to buy a $50 DMT to take care of what might be a $5 oilstone.
Anyway, get back to us and let us know whether it's a water or oilstone, and what the colors are. Once we have some idea of what the stone looks like, we can probably identify it and give you some idea of what it should be used for, and whether it's worth spending a lot of time on or whether, if it's cheap enough, it would make more sense to replace it. If you have a digital camera, pictures would make it easier.
Hope this helps,
BDL
PS. If you want to get into the differences between oil and waterstones, ask.
