Perform magnolia grafts in the spring. Examine the magnolia you wish to graft onto your shrub and make sure you can see buds and new growth. Cut off a small branch on the magnolia that's ½ inch in diameter; cut at the base of the branch with a grafting knife.
Select a branch of similar size on the magnolia shrub. This is called the stock and the branch you cut in step 1 is called the scion. Cut off the end of the stock branch so that it is about 2 inches long.
Cut into the green end of the scion diagonally to remove a sliver of wood so that you are left with a V-shaped groove. Do the same laterally into the end of the stock branch. Fit the scion and stock together, working one side of the "V" on the scion into the center of the "V" on the stock.
Hold the graft together so that as much of the green inside of one groove is in contact with as much of the green inside of the other groove as possible. Wrap the graft completely in grafting tape, beginning ½ inch before the graft and ending ½ inch past the graft and overlapping the tape slightly as you wrap.
Cover the tape well with grafting wax to keep out rain and other moisture. When you see new growth begin to appear on the outer end of the scion and the graft looks healthy, remove the wax and tape.