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1
Cut your peeled potatoes into whatever shape you like, but probably no skinnier than three-eighths of an inch. Rinse them and shake off the water (part of the genius of this technique is that a little residual water won't cause splattering, so you don't need to towel-dry the potatoes). Put them in a heavy pan - a straight-sided saute pan is ideal, but anything not too shallow will do. They should ideally be in a single layer, but this is not always practical: aim for it, though. Add room-temperature fat just to thoroughly cover and put the pan over low heat, without a lid.
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2
As the oil temperature slowly rises, the potatoes will, in effect, poach in fat and their excess water will gently evaporate (hence the lack of splattering). Yes, the oil will bubble, but reassuringly, not alarmingly. Every now and again, use a thin-bladed spatula or a long-handled spoon to make sure they are not sticking (their starch has a tendency to cause this) and give the pan a shake. Be very careful: at a certain point they will be very, very fragile - cooked but not yet crisp. I cannot help thinking of the nightmarish way a caterpillar liquefies in its cocoon before emerging as a butterfly.
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3
When the potatoes are very tender, you can raise the heat, but only a little. Say, from low to medium-low. They will finally start to crisp and turn golden, and will ultimately become french fries. Excellent ones.
