Large trees aside, there are many pruning jobs that you can do on your own. In all cases, the key is to prune the unwanted branch while protecting the stem or trunk wood of the tree.
Tree branches grow from stems at nodes and pruning always takes place on the branch side of a stem-branch node. Branches and stems are separated by a lip of tissue called a stem collar which grows out from the stem at the base of the branch. All pruning cuts should be made on the branch side of this stem collar. This protects the stem and the other branches that might be growing from it.
It also allows the tree to heal more effectively after the prune. To prevent tearing of the bark and stem wood, particularly in the case of larger branches, use the following procedure:
Make a small wedge shaped cut on the underside of the branch just on the branch side of the stem collar. This will break the bark at that point and prevent a tear from running along the bark and stem tissue.
Somewhat farther along the branch, starting at the top of the branch, cut all the way through the branch leaving a stub end.
Finally, make a third cut parallel to and just on the branch side of the of the stem collar to reduce the length of the stub as much as possible.
A similar procedure is used in pruning one of two branches (or one large branch and a stem) joined together in a ‘u’ or ‘v’ crotch. This is known as a drop crotch cut.
Make the first notch cut on the underside of the branch you’re pruning well up from the crotch.
For the second cut, cut completely through the branch from inside the crotch well up from the ridge of bark joining the two branches.
Finally, to shorten the remaining stub, make the third cut just to one side of the branch bark ridge and roughly parallel to it.