Grafting is an old horticulture technique where a twig from an established tree is attached to a younger tree. The grafted twig grows into the bark and becomes a permanent part of the tree. This allows one tree to grow a variety of different fruits, or nuts in the case of a walnut tree. The grafted branch retains the qualities of the original tree. Make sure the walnut twig you use for the grafting is of a related species to the tree you are grafting to.
Cut a twig from the tree you wish to graft into your other tree using the scalpel. This is called the scion wood. Collect the scion wood while it is dormant. Mid-March is the best time to collect your sample. Check that the scion has buds on it from last season's growth. The scion should be 4 to 6 inches long.
Dip the end of the scion branch into the melted paraffin wax and let it dry. Wrap a wet towel around the end with the wax. Put the twig into a plastic bag and seal it. Place the bag into the refrigerator. You will graft the scion when the tree buds in early May.
Choose a branch that is double the thickness of the scion branch for grafting. Make a cut that is about 2 inches long vertically. Make another cut horizontally to make a 'T' shape along the vertical cut. Where the two cuts intersect use the edge of the knife to gently lift up the bark without breaking it. Cut away the wood from the last 2 1/2 inches of the scion branch so that the underlying wood is exposed.
Put the exposed portion of the scion under the bark you lifted at the intersection of the two cuts. Put two nails into the bark to hold the scion in place. Cover the area of the graft with grafting wax, which can be purchased from a garden center. Place aluminum foil over the cut surface and tape a plastic bag over the scion. Take away the plastic bag once the graft has healed.