Grasp the basics principals of grafting before you begin the procedure. Understand that for two plant pieces to grow together, you must press the cambium layer -- the green layer of wood just under the outer bark -- of one against the cambium layer of the other for a sufficient period of time to allow them to meld. Most of the preparation for grafting includes assembling the tools and materials necessary to accomplish this.
Choose the type of grafting you intend to try for your debut from among the many different methods developed. Opt for one of the simpler procedures, such as whip grafting or cleft grafting. Use whip grafting to join a root stock and a scion of equal diameters; use cleft grafting when the scion is significantly smaller than the root stock.
Assemble a garden clipper and a knife with a sharp, slender blade for either type of grafting, together with a clean rag and denatured alcohol to sterilize the blades. Obtain grafting glue and grafting tape. For cleft grafting, add a sharp garden saw, a clefting tool wedge and a mallet to split the stem of the root stock.
Select the scion parent from the cultivar you desire to reproduce, choosing a vigorous, healthy plant. Select the root stock from a species closely related to the scion that grows well in the climate and soil of your yard; pick a healthy root stock about 1/2 inch or less in diameter for whip grafting, one up to 4 inches in diameter for cleft grafting.
Mark grafting day on your calendar, choosing a day in late winter or early spring when both the root stock and the parent of the scion will be dormant. Schedule sufficient time so that you can complete the graft in one day, everything from cutting the scion and the root stock through securing the graft with grafting glue and tape. Avoid watering or fertilizing the trees before grafting since dormant trees cannot absorb nutrients.