First, wash your potatoes. Once washed, you may peel the potatoes, but generally, I just leave the skins on. More nutritious this way and it eliminates a step if you do not peel them. Now, get your mandolin out. If you do not have a mandolin, here is one for less than $20: Norpro Mandolin. Just slice your potatoes. I use the "medium slice".
Once they have boiled for 3 minutes, drain them and run cool water over the potatoes to stop the cooking process. Then just lay the potatoes out onto your dehydrator trays and dehydrate. I turn on my dehydrator on before I go to bed and the potatoes are done the next morning. BTW, here is the dehydrator I use: Oster 4 tray dehydrator. Don't let the low price (under $50) fool you. I have had mine for 4 years and use it a LOT and it still works like a champ.
These actually are peeled but like I said previously, generally, I don't even bother to peel them. To reconstitute, just take the desired amount of potatoes and place in a pot or bowl and add enough of really hot water to cover the potatoes. Let set 10 minutes and they are ready to use. These can be added to soups, stews, or casseroles or you can pan fry or even mash for mashed potatoes.