Cut a length of the new cultivar tree branch with two to three buds. This is called the scion. Choose one that's a fourth inch to a half inch in diameter. Make a 1- to 2½-inch slanting cut at one end. Cut again in the middle of the slant to form a slight split. This cut exposes the cambium layer of cells underneath the bark. The cambium layer grows new cells that attach to the rootstock-branch cambium layer. The rootstock, or understock, is the part of the graft that produces the root system.
Choose a fourth-inch to half-inch-diameter rootstock branch. Make a slanted 1- to 2½-inch cut with the sharp knife. Cut again to form a very small split in the middle of the slant. Press the splits of the scion and the understock tightly together. The cambium layers are now touching, and the cells will attach. Wrap the entire area tightly with grafting or electrical tape.
Remove the tape one month after new growth has begun on the scion. The tape may have disintegrated already. Do not prune newly grafted branches for one growing season. Pinch back tips of new branches to stimulate growth.