Peaches and nectarines are skinned by blanching briefly in boiling water. Use freshly boiling water and blanch only a few at a time. If too many are placed in the pot they will become soft and slightly cooked.
Score a cross on the base of the fruit and stand on a slotted spoon. Immerse in boiling water for roughly 10-20 seconds, then transfer immediately to iced water.
The edges of the skin where you scored the cross shape should be curling slightly. Starting here, peel back the skin. It should come away from the fruit easily.