I bought roasted peanuts from the market and they have too much salt in them.
How should I reduce the salt in those peanuts as much as I can?
My intent is to make peanut butter.
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Depending on how much salt is on them, and how it's been applied, you might be able to knock some of it off, and effectively decant it:
You save yourself some effort, you might be able to do the whole work on top of your washing machine, or leave the container in the trunk of your car for a few trips. The larger the salt crystals, the easier this will be to remove. If it was applied as a wet spray or while the oils were on the surface of the peanuts, it's going to bind more to the peanuts, and be more difficult to remove.
Although the diluting trick will work, you can also use the peanuts in a recipe that would have otherwise called for salt and leave out the additional salt. You could also crush them up and use them as a topping for something that could use a little extra salt. (ice cream, Pad Thai, etc.)
I have rinsed salted nuts well in water to remove the excessive salt and then dried in the oven. Since salted nuts are already roasted, they don't "roast again" very well at all (or in general behave like raw peanuts when cooked) but you can certainly rinse to remove excess salt and dry at low temperatures.
If you want to just eat them immediately you can just eat them damp, but to preserve the quality or to use for something like peanut butter, they need to be dried again.
Getting them unsalted in the first place is more desirable, but not always feasible due to oddities of pricing (where unsalted nuts may cost 2-3 times as much as the same things with salt.)
Bring a saucepan of water to the boil, then add the peanuts and a small potato and simmer for half an hour. The salt will travel from the surface of the peanuts into the potato, which you can then discard. Since the peanuts are for peanut butter, boiling them shouldn't affect the final taste, though you can try a lower temperature if you're concerned, or if you want to preserve crunchiness.
I used to use this method when boiling super-salty gammon steaks. In this case, it should actually be more effective, since the salt is only on the surface of the peanuts, rather than begin suffused through them.
For eating in general,
I prefer to do this few at a time, than the whole 2.5lb container. Here are some pics. https://drive.google.com/open?id=0Bzj_F7fR53q6NnlfanpmUloyWlE
You could put them in an industrial sifter and use that to knock the salt off and separate the peanuts from the salt in one step, but that's probably overkill unless you have a lot of nuts. Instead knock the salt off first, either with the shaking method that Joe mentioned or by placing the nuts between two sheets of clean fabric or clean, food safe paper and rolling and gently scrubbing them. Then do the sifting step using a normal kitchen sifter/strainer.
I found that a nylon mesh strainer isn't abrasive enough, hardly removed any salt. A metal one works very well so it's my "go to" tool. Not all the salt is removed but enough to make them edible and not overly challenging to my autoimmune situation until the too salty nuts are gone (too expensive to throw away) after which I won't buy salted nuts anymore. Also, I'd de-salted probably 2 pounds at a time, and will also try re-sieving smaller handfuls when I actually go to use them in a dish. And cashews are harder to desalt as thoroughly because of their inner curve, but are still greatly improved. Thanks for raising and addressing the problem.