There have been a number of discussions about grafting. I have done a lot of it and have taught classes for friends, neighbors and garden groups on the different grafting techniques. That is why we are going to post video as soon as Tony has the time to film it. Tropicdude hit on one of the most important points. Roughly 50 percent of the success comes from the condition of the budwood. No matter how good your grafting skills are, bad budwood means bad results. Budwood conditioning is the first thing on the list. I am attaching some pictures to illustrate the tools you need and the process. I figure I can help a few people this way who don't want to wait for the video.
Picking good budwood is easy. First choice for me is always those blossom panacle branches that failed to set fruit. They are big and have a good swirl of leaves at the end. A hardened off new growth swirl is my second choice. First step is just like Tropicdude said. Clip off the leave back about 10 or 12 inches from the end. Make sure you leave a little leaf stump though.
The little leaf stumps will drop off in 4 or 5 days with this heat and then the bud will start to swell. They will turn bright green and get fat. That is your signal to get your grafting stuff together.
Along with the obvious grafting supplies like tape and clippers that you will need. There are a few more things in the tools picture. The reason for the bow saw is if you want to top work a tree. That is another class though. Note the leather glove. If you are right handed use a leather glove on your left hand. If you are a lefty, do the opposite. That tool is to keep you out of the emergency room. One slip with a sharp grafting knife or in my case, a razor blade, will really mess up your day if you don't use that little extra protection.
I have also included a picture of my home made grafting table. When you graft 40 or 50 Seedlings at a setting, your back will kill you unless you work at a comfortable height. None of this bending down grafting at my age. The use of my grafting bench also allows me to graft very young seedlings with out breaking the tops off. Note the one in the picture. It is less than half the size of a pencil. I like that size. For this size seedling I use a unique graft. It is a combination of cleft, veneer and butt graft. I don't worry about matching budwood and seedling stem sizes with this graft. I just pay attention to one side and the take rate is nearly 100 percent. I have attached a sketch of the graft, sorry for the artistry. I am saving the little root stock tree for the video. I hope this will help some of you new grafters.