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 California Avocado Commission recommends this (safe but wimpy - see below for a better way) three-step process:
Start with a ripe avocado and cut it lengthwise around the seed. Rotate the halves to separate.
Remove the seed by sliding the tip of a spoon gently underneath and lifting out. The other common seed-extraction method - striking the seed with a knife and twisting - requires some skill and is not recommended.
Peel the fruit by placing the cut side down and removing the skin with a knife or your fingers, starting at the small end. Or simply scoop out the avocado meat with a spoon. Be sure to sprinkle all cut surfaces with lemon or lime juice or white vinegar to prevent discoloration.
Another (and my favorite) way to remove the pit is by holding the half with the pit in one hand and striking the sharp edge of the knife used in step one into the pit, then twisting to remove. This is the "pro" way to do it, but takes a little practice. The video Nate referenced in the comments shows how to do it, it's not that hard.
If you're going to be chopping the avocado up, you slice it up using the tip of the knife still in the shell, then scoop the sliced avocado meat out with a spoon.
Best Answer
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