You can, of course, eat a fresh peach right off the tree. Much better with the fuzzy peel off. When they're really ripe and ready those peels just lift right off like Elmers glue you probably squirted on your hand back in elementary school and then lifted off when class was not too exciting.
If you're looking for more ways to use your peaches, then I have my Southern Peach Pound Cake pasted up. Yum. That's a good one.
You can also make peach jam using the same recipe I use for my strawberry jam. It's a quick micowave recipe that requires only 2 cups of fruit (chopped up fine). No canning. You just keep it in the refrigerator where it's fine for several months.