Five steps to pruning anything refers to not only trees but also bushes and other woody plants. Here are the five steps.
Step 1: Remove all dead branches. Also look and remove unrepairable, dying, damaged, and diseased branches.
Note: Trees do not have the ability to head similar to you and I. They encapsulate to cover a wound but never heal in a traditional sense. (I have written a blog about this, Tree Autopsy: How do Tree "Heal"?)
Step 2: Establish a dominate leader (or your desired structure). In this process you select where you want the plant to grow. In most trees you want one stem that originates at the trunk and grows straight up through the center of the tree out the top.
Step 3: Establish the lowest permanent branch. We want to know the lowest branch that at some point in the future will the the lowest branch. It may not be the lowest branch today but it will effect how we prune the tree today.
Step 4: Establish our scaffold branches. Scaffold branches are the permanent branches that will be the structure of the mature tree. We need to select branches that are spread at least 18" apart for larger trees and spaced evenly around the parameter of the tree.
Note: It may be helpful to mark these branches so you can be coherent in your trimming from year to year.
Step 5: Subordinate, or reduce, branches that are not the leader, lowest permanent branch, or scaffold branches. This is to guide the tree to provide more energy to the branches that we want to keep. The branches that we are subordinating will eventually be completely removed.
Triming a tree sounds easy until you start looking at a tree and realizing that you have a lot of hard decisions to make. This is understandable. Take your time. Be willing to change your mind as time goes along, as you may be forced to via wind and ice damage.