Grafting non-woody plants
such as: Cactus, succulents like aloes, jade trees

Use a clean, very sharp instrument for all cuts.  The sharper, the less dammage to the tissue.  A
 
 

brand new single-edged razorblade is excellent.
To start, make sure the stock and scion are hydrated, as your success rate will be greatly
improved.  For succulents like cactus, that just means fat!  Cut the top off the scion (or branch for jade or aloe) and locate the vascular tissue.
In cactus it is in a ring tward the center.  In jade it's a cambium layer under the thick skin.
 

Cut the bottom off the scion, and locate it's vascular tissue too.

In the illustration, we've shown the vascular ring in a cerus stock (a tall skinny cactus) and a mamilaria scion (a small
 
 

round cactus)
These rings MUST touch in at least one place for a sucessful graft.Note:  your finished graft will rarely be centered, due to the variation in ring placement in individual plants.