Start with fresh, ripe peaches. They should feel heavy for their size, have a bit of give near the stem (or stem end), and they should smell like peaches. If you're not confident in your ability to choose a ripe peach, see How to Buy Peaches.
The focus here is peeling whole peaches, and I find it's the best way to peel more than a single peach or two. If, however, you only have one or two peaches to peel, I recommend peeling them after you pit and slice them. See how in How to Slice Peaches.
For greater numbers of peaches, however, the first thing to do is to bring a pot of water to a boil - if you have a pot large enough to hold all the peaches, use it; if not you can easily work in batches, so no need to worry.