Answer: Grafting can be simple or quite involved but is basically a process where a part called the scion is taken from one plant, and is attached to a second plant called the stock. The scion may be a single bud, a small twig bearing a few to several buds, a piece of stem, a terminal shoot, or a fragment of root of a desirable variety.
Many kinds of grafting are practiced by nursery growers for special purposes or with specific plants, but those best suited to the average gardeners needs are whip, cleft, side and bridge grafting.
Here's a website complete with photos to help you with your grafting:
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