Yes I do know a little about grafting.
The best time to do it is in the
spring.
There are a few different ways to go about it.
There is the Flat graft,
seedling graft,the side graft,the cleft graftand the stab graft.
I think the one you have is the flat graft. I'll try to explain it best I can.
To make a flat graft slice off a healthy scion (top of
cactus) of a diameter to match the stock (the piece being grafted on) then bevel the cut end of stock slightly. Remove the top of the stock and bevel the edge downward so stock and scion will stay snugly together.
When both pieces are ready,remove a final thin slice from each part. Press the pieces together with rings carefully matched. (rings liek you see when a
tree is cut down) Drape strings weighted with hardware nuts or fishing weights over the top of the grafted pieces. Keep the
plant dry and out of direct sun until the parts begin to grow together,then remove the strings.
hope you are able to follow that