It can be done -- just remember:
"Peaches from seed can result in trees that bear decent fruit, although they may not look or taste just like the peach from which the pit came. Most commercial peach varieties are budded onto specific varieties of rootstock."
Check the first link below for the information you need on planting and watering specifics. This is how to do it if you live in a climate that has a true winter, but is not so cold that it will kill a peach tree when grown, so that your effort is wasted.
However, if you don't have a true winter in your area, you need to "break" the dormancy of the seed artificially. From the Growing Edge:
"Peach stones need to be stratified before they will germinate. This means taking the peach stone directly from a ripe peach, soaking it for 24 hours, then wrapping it in damp paper towel and then plastic (or in a bag of damp, sterilized sand, which is the procedure in the nursery industry), and placing this into the refrigerator at about 3-4 deg. C for a period of four months. This replicates what would occur in nature: The damp seed from the fruit falling on wet ground and then going through a long, cold, damp winter, which will act to break the dormancy the stone has when taken from the fruit.
When conditions warm up again (when you take the stone from the refrigerator) and sow it into potting mix at about 20-25 deg. C, it will then be ready to germinate. Germination, however, could take some time as the hard seed coat makes the process of germination rather slow. Once you have your peach seedling, its a good idea to graft it onto a good variety (a shoot with buds taken from a good cultivar of fruiting peach) since seedling-grown peaches don't often produce very good quality fruit compared to the varieties of peach you can buy from nurseries (which are always a rootstock with a good fruiting type grafted on top). Good luck with the peach stones. [Note temperatures are in Centigrade, not Farenheit!!]"
And I wish you good luck as well! Sweet eating -- a few years from now.