There are two trees involved.  The donor tree must be identified and, if not your own, permission must be given to take a branch. Keeping it in water to take to the graft site may be needed.

All action thereafter is on the recipient tree.   You must chose the limb to be grafted and saw it off just above the desired level so that if the bark tears the stripped part is above the level desired.  The cut is the made  at the optimum level and the cut surface cleaned with a paring action of the knife.

A piece of twig is prepared to act as a separator to cleave the bark from the cambium of the host tree.  Nothing special but it should be a narrow 'V' shape 10 to 14 cm long.   A vertical cut is made down the branch at one, two or three points around the cut surface according to how many grafts are to be inserted.  The slit is then widened along the cleavage of the cambium to take the graft.

The graft is then prepared.  It is cut from the branch taken from the donor tree and should have four or five buds above the level inserted.  Below these buds a tapering sliver of wood is sliced to leave a  length of bark exposing the cambium. This is inserted into the slit already prepared.

The wound is bound firmly with cord.  The open cut area is then covered with clay and a retaining cloth with holes taking the grafts is strapped over the whole graft site.

This is the end of the human activity.  The rest is for nature.  In a few weeks it will become apparent if the graft has taken.  Small buds will develop followed by leaves and a healthy growth.

As the summer progresses the graft swells and it has to be  watched.  The top may develop too fast and need to be trimmed while the union is strengthening.  It may also be wise to release the tightness of the binding to prevent damage from constricting the expanding tissues and a splint may be needed to support the graft when the wind blows.

All this is a matter of judgement and experience, but that is the wisdom acquired from the traditional farmer or your own instincts.  Failure one year is the basis for improving techniques next year.