Step 1

Find a seedling or pup to use as the scion.  Find a suitable rootstock for your scion.

Step 2

Sterilize a razor with alcohol and a flame.  Make sure your hands are clean.

Step 3

Take the root stock and slice the top off.  If it is a ribbed stock cut the ribs at an angle to prevent cupping after it dries out.  Take the chosen seedling and slice off a good portion of the top.  Place the seedling onto the stock and match up the vascular bundle with that of the seedling.

Here are some that are still grafted and the rest are various cacti that have been degrafted.
A look at some successful grafts. I keep them indoors under low light until they are healthy enough to go outside. It normally takes a month or so before I move them out.
These are some that have been moved outside.