What is the best/easiest method to peel peaches?
By far the easiest method is to use a pan of hot water and a bowl of ice water. Essentially, bring a pan of water (enough water to cover the peach to a boil. Meanwhile, with a sharp knife, make a small 'X' shaped incision in the top and bottom of each peach.
When the water is boiling gently place a few of the peaches into the water and simmer for around 20 seconds, just until the skin can be seen coming away. At this point use a slotted spoon to remove the fruit from the boiling water and place them in the ice water. After 20 or 30 seconds you should be able to remove the skin with your fingers.
The same technique is used with tomatoes
I know of two techniques: you may blanch the peaches or you may use a serrated peeler. Blanching the peaches makes it easier to peel them. Make a cross on the top of the peach, dip it into hot water for 30 seconds, remove to ice cold water, pull off the peel. Blanching may impart a slight cooked flavor to raw peaches.
Another technique is to use a serrated swivel peeler. These look like the regular peelers, but with serrated blades. Peeling a soft peach or tomato with a serrated peeler is just as simple as peeling a potato with a regular peeler.