Peaches will turn brown if you let them sit out long enough, whether inside a refrigerator or on a kitchen counter top.
There are a few things which you will be able to do in order to keep them from browning, such as making sure that you get only the freshest peaches from your local market and refrigerate them as soon as you get them home. You will also want to consider peeling the peaches over a bowl so you will be able to get every simple drop of juice that comes out.
After you remove the stone, you will be able to leave halves together or slice them to whichever size you desire. You will also be able to sprinkle each of your peaches with sugar and put pieces of them in a colander so you will be able to drain them over a large bowl with the juice, stirring off and on for around twenty minutes or so.
When you are mixing the peach juice, remember to throw in a little bit of lemon juice. In the end you will want to cover everything in a very tightly-sealed container so they stay good for as long as possible.