Included Unions
Research shows that trees with multiple trunks - a trait referred to as codominance - have a higher likelihood of failure than those with a single trunk. Unfortunately, landscape settings like parks and yards tend to foster codominance.
Trees that tend to grow a single trunk in a shady forest often develop a host of codominant stems when planted in more open settings. Consider the forest-grown Oaks (below left) compared to the open-grown Oak (below right).
A risk with codominant stems is "included unions" in which a seam of bark gets trapped between multiple tightly spaced stems or trunks. Below left is a tree that divides into two trunks pressed up against each other. Below center is a similar tree bisected, with bark visible in the interior. Below right, purple brackets illustrate how codominant stems often have relatively little material holding them together at the base of the union.
It's not hard to imagine how two stems with little material at the base of the union, a lot of weight above, and a seam of bark in the middle could fall apart relatively easily. This is why an image search for something as vague as "broken tree" turns up a huge percentage of failed included unions:​
Preventing Included Unions in Young Trees
The best way to prevent codominant stems is to prune the tree while it is young to a cultivate a dominant leader. Structural pruning can begin a year or two after planting and continue every few years as the tree matures. Structurally pruning a tree several times in its youth can nearly eliminate included unions. This reduces the chance of a tree falling apart later in life and is less expensive than remediating structural vulnerabilities in mature trees.
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Solutions for Mature Trees
Structural pruning may not be an option for mature trees because it would entail making large cuts that adversely affect a tree's health. Included unions on a mature tree are often better remediated with support systems such as cables or rods that are installed between codominant stems. These systems reduce loading on weak unions.
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Whatever age your tree, included unions should at least be inspected to gauge if remediation is warranted.
Then step back and try to see each tree for the incredible idiosyncratic wonder that it is:
Holdinging all of these things, a vision and direction will begin to emerge. This will lead to scores of individual decisions. Add to that, years of practicing the physical techniques required.
That's how to prune a tree.