A bit late, but a visit to the in-laws reminded me that I'd given them some trees that I didn't have duplicates of myself. This is a scion of Ard Cairn Russet that I'm trying on a M27 sucker (as the parent tree is very vigourous on M26).
First make slanting cuts on both scion and rootstock, taking care to select wood of similar diameter and making the cuts of matching length/angle.
Then make a triangular 'tongue' in both ends, so that the different bits of wood can be interlocked. This is best done against a hard surface, rather than by holding in one hand and pressing down, which can result in rather nasty finger wounds. It's a good idea to do one first, then use the first as a guide for the second cut, as it can be difficult to rectify mistakes.
Next, interlock the two pieces together. If you have done it carefully, the match should be exact.
Using a special material (ultra-low tack duck tape, only available from the very cheapest £ Shops; I recommend HyperValue in Swansea) carefully cover the union, making sure you cut enough tape to cover both ends. Press the pieces together as you wrap to ensure as much contact between the pieces as possible. Low-adhesiveness of the tape is quite important, as really sticky tape will pull off the bark later on when you want to remove the tape. Really cheap stuff sometimes just comes loose with weather after about 6 months.
Finally, use clothes pegs to exert gentle pressure to union, making sure that it presses against the cut surfaces.