First and foremost, walnut grafts are different from most other trees because the most successful scion is the large terminal bud. The second thing is that an inlay side graft is more successful than most other grafts because it avoids bleeding. So pick your scion carefully and trim it with a 2 to 3 inch slant cut similar to what you would make for a whip & tongue graft. On the back of the scion, make a similar cut about 3/4 inch long so that the cambium is exposed on both sides. Now hold the scion up to the bark or a 1 to 2.5 inch diameter walnut seedling. The graft should be about a foot high, no more than 2 feet above the ground. Using a sharp sheep foot knife, cut on each side of the scion through the bark. Put the scion aside and make a downward slanting cut across the two lines you just made at the very top of the cuts. The purpose of the slant cut through the bark is to allow the scion to set in the groove tightly. Now use your blade to pull the bark flap out from the trunk about an inch. Push the scion into the groove until it is entirely covered by the bark flap. Cut the bark flap off so it just covers the 3/4 inch cut on the back of the scion. Use two wire nails no more than an inch long to nail the scion to the trunk. One nail should be near the top of the graft cuts, the other nail goes through the bark flap and into the wedge part of the scion. Don’t nail too tight, just enough for a snug fit. Cover with beeswax or other graft sealant.
Aftercare is crucial. Exactly 10 days after the graft is made, cut the top of the tree off about 2 feet above the graft. The stub will help prevent bird damage and will give a support to tie the growing scion so it does not get blown out by high wind.