Main branches should be spaced around the trunk with space between layers of branches. There should be enough space between branches so that they do not grow into each other. Typically about five major branches are selected each year as the tree grows in height. Side branches that grow off the major branches are selected in the same way as the major branches. Branches that grow straight up or at a narrow angle with the trunk or grow toward the center of the tree are removed. Outward growing branches are selected to remain as long as they do not grow into other branches.
Another system sometimes used for peach trees is the vase shape system with three to five major branches or trunks originating from the lower part of the tree. Side branches from these main trunks are selected similar to the central leader system.
Most branches are removed entirely back to the trunk or major side branches. Extra long branches may be shortened by pruning just above a bud. Make sure the bud is pointing in the direction you would like the branch to grow, usually outward at as horizontal direction as possible.
If you have not pruned enough previously you may need to remove some of the larger branches that are crowding or growing in the wrong direction.
Sometimes rather heavy pruning stimulates some regrowth of multiple branches that grow straight up in June. These are referred to as water sprouts. The best time to remove these sprouts are when they are still soft and less than 12 inches long.
The best way to remove them is to snap them off rather than pruning them.
Grab them with your fingers and jerk quickly sideways or down. The base of the sprout contains latent or hidden that may be stimulated to grow another sprout to replace the one you removed. Snapping removes the base, which is not removed with pruning. If sprouts are allowed to grow they will shade the inner and lower branches, reducing the size and quality of the fruit.