Remove the peach scion from the parent tree in winter while the peach tree is dormant. The scion should be 1/4 to 3/8 inches in diameter and long enough that the trimmed scion will have at least three buds.
Store your scion until you are ready to graft, by wrapping the bottom end in moist paper towels then loosely wrapping the entire scion in plastic. Store at 34 degrees F.
Select peach rootstock about the same diameter or slightly larger than the peach scion. Either plant directly in the ground in a greenhouse, plant in a container slightly larger than the root ball and grow in a greenhouse or plant outside in partial sun in a space that has protection from wind and severe weather.
Choose a spot on the rootstock that is blemish-free and about 3 to 4 feet high. Cut the top of the rootstock off.
Using a grafting chisel, carefully split the trunk. You are looking for a 3- to 4-inch long split in the middle of the trunk.
Trim the tip of the scion at an angle about 1/4-inch above the top bud.
Trim the bottom of the scion into a 1 1/2-inch wedge. Trim both sides of the scion removing the outer bark to expose the cambium underneath.
Using the grafting tool, gently open the split in the rootstock trunk and insert the scion wedge. Make sure that the cambium of the rootstock and the cambium of the scion touch.
Cover the graft with grafting compound.
Wrap the rootstock and scion with grafting tape. Start below the bottom edge of the split on the rootstock trunk and work your way up to a point above where the scion is inserted into the wedge. As the grafted tree grows, the tape will disintegrate.
Understand that you can allow growth from below the graft to grow during the first season. This growth is from the rootstock and provides additional energy to the grafted tree. Do not allow the growth from the rootstock to shadow the scion.
During the second growing season, cut off all growth from the rootstock. Your grafted peach tree is ready to be transplanted to its final growing location.