Scrub your potato and dry it with a dish towel. Do not peel.
Slice the potato as thin as you can on your mandoline slicer. Try the 1/8 inch setting. The slices should come out whole, but very thin and flexible.
Put the slices into a bowl and drizzle with just enough olive oil to coat. Use your hands and make sure every slice is coated.
Put a piece of paper towel or parchment paper on the carousel of your microwave and lay out a single layer of potato slices.
Microwave for anywhere from 2 1/2 to 4 minutes, depending on your microwave, how big your potato slices are, and how thickly you sliced them. Watch through the window and when they turn evenly golden brown, they're done. Stop the machine to check on them if necessary, and pull out any chips that brown earlier than the others. Repeat for the rest of the slices, and you can reuse your paper liner.
Sprinkle with sea salt, freshly cracked pepper, or any other herb blend you like.
Microwaves vary, mine is a standard 1000 watt with a rotating carousel. Your cooking time may be slightly different depending on the power of your microwave, and how thin you have sliced your potatoes. Check their progress through the door window and don't hesitate to stop the machine and pull them out when they turn golden.
You can use all kind of potatoes and other root veggies for this, such as sweet potatoes, purple potatoes, beets, parsnips, etc. *UPDATE* I tried this with beets and it did not work, they burn before they crisp.
If you want to slice your potatoes ahead of time, immerse them in a big bowl of cold water to keep them from turning brown. You'll have to thoroughly dry them on a clean kitchen towel before coating with oil. Note that the soaked potatoes did take longer to crisp up, about a minute more, on average for me, but otherwise they were just as good.
The chips will shrink up considerably as they cook, so plan accordingly. In other words, make lots :)
This seems to work best when you place the parchment or paper towel right into the microwave, without a separate plate to hold the chips. You can use a plate, but it absorbs some of the energy and the chips cook more slowly.
Can you use spray oil for these? Yes, and if you're counting calories that's a good idea, but I do think that a good olive oil pays off in terms of flavor.