In the January/February 2009 Hobby Farms, you can read an article discussing the benefits and various ways to graft plants. Here are more diagrams of grafting approaches by Rick Gush for you to try.
An approach graft, which united two unsevered stems, is used by arborsculptors to produce joints, by bonsai growers to add a branch where none exists and by horticulturists to bypass damaged areas.
This is the type of graft that occurs spontaneously in nature when stems or trunks press together.
Inarching live bridge grafting, is used to bypass a damaged area of a tree trunk.
The scion can be an existing shoot or sucker, or can be a new plant planted alongside the damaged tree.
Plants with thick bark are often patch budded. Budding is done while the plants are actively growing, so their bark slips easily.
A rectangular piece of it is removed from the rootstock and then covered with a bud and matching piece of bark from the scion.
This budding method can be used when the bark is not slipping.
Any interior wood should be removed from the scion bud before it is fitted into the matching notch in the rootstock.
This is the most commonly used budding technique, and is performed when plants are actively growing.
The whole bud piece of the scion is slipped into a pocket cut into the rootstock bark.
This is one of the most common methods for changing fruit variety on a mature fruit tree.
This graft is used to produce particularly strong unions on small fruit tree rootstocks.