Collect scion wood from plumerias when the plants are less than 1 year old. Cut branches with multiple buds that are at about 6 inches long and slightly smaller than the rootstock to which you will graft it.
Trim the bottom of the scion into a wedge that is at least 3/4-inch long.
Prepare the rootstock by removing any branches that remain. Cut the stock flat and make another cut through the diameter of the rootstock that is about 3 inches deep.
Insert the freshly cut scion into the cut in the rootstock so the exposed flesh on the wedge-shaped bottom is in contact with the inside of the cut portion of the rootstock -- the graft will not succeed if the exposed parts are not solidly connected.
Wrap the graft with grafting tape, forcing the cut area into tight contact with the scion. Use grafting wax to seal the top of the rootstock.
Cover the grafted plant with clear plastic if the plant is at risk of drying out while the graft is healing.
Check regularly for the scion to begin putting out new leaves, indicating the graft has succeeded. Remove plastic, wax and tape once you are certain.