With a paring knife, cut an "X" through the skin in the bottom of each peach.
Bring a medium or large pot (depending on the number of peaches) of water to a boil. Fill a large bowl with cold water and some ice. Do this step now so it's ready to go when you need to dunk the peaches.
Place the peaches into the boiling water for 45 seconds. If you leave them much longer, the peaches will start to cook and soften.
Using a slotted spoon, lift the peaches out of the water and immediately transfer to the bowl of ice water. Let the peaches sit in the ice water for a few minutes to cool.
Starting at the "X" on the bottom of the peaches and using your fingers or a paring knife, peel off the skin from each peach.
Notes
Use the same method whether you're peeling one peach or ten. Adjust the size of the saucepan and bowl as needed.