at its essense, grafting is just the whittling of wood joints (done with live wood of matched size and at a specific time of year). The layer of tissue just below the epidermis (the cambium) is really the only important part of the equation, for this is where moisture, minerals, and sugars are transported within the plant body. If even a small section of cambium is in contact, the plant will be able to repair the damaged tissue along the border and heal the two pieces as one. The moves must be practiced and the tools laid out within reach, for the whole operation must be completed as quickly as possible, preferably in under a minute (contact with the air will dry out the cambium of both rootstock and scion = death).
that said, its a relatively straightforward process that still doesnt seem like it should be possible. Ive got a few years practice, so i went big this year and i completed over 115 grafts of some 40 species. It was a monumental undertaking, and ive been thrilled to watch the dormant buds open up and absolutely gush with leaves, flowers, and woody stems.
ill have to tend the joints for the next few months to ensure the sealant doesnt open up and dry out the union, but soon enough my yard (and my face) will be covered with apricots, nectarines, plums, peaches, apples, pears, and cherries... yea!
heres a couple links to showcase several types of grafted joinery:
http://www.ces.ncsu.edu/depts/hort/hil/grafting.html
http://www.extension.umn.edu/distribution/horticulture/components/DG0532c.html
