In order to grow a hybrid plant, you will require two things. Rootstock, on which the hybrid will actually grow, and a source for the stem of the plant.
When you look at any hybrid Japanese maple, you will see a graft at the base of the plant. This is evidence that the plant is, in fact, a hybrid and not just a lucky seedling.
The rootstock used is generally the hardy basic acer palmatum. These plants are very easy to grow, and should you be entertaining the idea of trying your own hybrids, you would be well advised to grow several dozen from seed to use as your rootstock.
There are several different ways to make the actual graft, and the method described here is the most common one, the side graft.
The rootstock, or understock of choice will be a two year old seedling. The scion, or short piece of shoot from the parent hybrid, may be one or two year old wood. One important thing is that the diameter of the understock and scion ideally should be as close to identical as possible. The reason is that as much of the cambium layer as possible needs to match up.
It is this cambium layer, or the very thin layer between the bark and actual wood of the plant, which will carry the nutrients and moisture. The more of the cambium layer that matches between the understock and the scion, the better and stronger the plant will grow.
To prepare the understock for grafting, cut the shoots back to about 6" in the winter when the plants are dormant. The actual grafting is usually done in January, when growth becomes stimulated. However, this may vary widely in your area, and in fact there is even a method for summertime grafting.
The scion should be collected immediately before grafting. You can use terminal shoots between 1" to 8" long. Aim for 3 pairs of buds on the scion.
Great care must be taken when doing the graft. Using a new razor blade on the understock, make a slicing cut downwards at a steep angle until you are roughly 1/3 of the way through the wood. This is done very low down on the stock. Remove the upper 2/3 of the "flap" on the outside of the cut.
With scion in hand, or on the bench, make a slicing cut at the bottom, matching the angle of the understock cut as closely as possible. Then remove a very small amount from the end of the scion, leaving a somewhat stubby point. Insert this point into the understock, and try to match up as much of the two cambium layers as possible.
Using grafting tape, or budding rubber, or even cotton thread, tie the union together very carefully. It is important to note that the cambium layer not be harmed, as this will result in a lost plant. The union should immediately be covered with beeswax or paraffin, or a grafting wax emulsion made for the purpose. The idea is to prevent exposure to the air and to promote rapid healing of the union.
As winter turns into spring, you should start to see your young tree sprouting new growth, a sure sign of your success!