Determine which magnolia will be the main tree, or root stalk, and which you'll only take a piece from --- the scion. Both magnolia plants must be healthy and just leaving dormancy.
Make a square cut around the leaf bud of the magnolia scion, and gently pull the leaf bud off the tree.
Make a square cut of equal size on the root stalk.
Place the scion into the root stalk, trying to match up as much of the cambial layers --- thin green layers --- as possible.
Wrap the tree with grafting tape, leaving only the leaf bud exposed. Wrap as tightly as you can to hold the scion in place.