Here's an illustration I did a few years ago, on a now defunct site
Just get through the cambium (remove all the green) and you'll be fine. You don't need (or want) to remove much else. Another thing to keep in mind: make sure you keep the entire exposed area of wood protected from the external air. Otherwise, the xylem can dry out and the layered branch will not receive sap, and will die.
Hope this helps!