A good start is to make sure you plant your new trees properly making them less vulnerable to stress. Research the species of tree you are planting and try to give it adequate shade and sun. Also make sure the tree will have room to grow. After planting place mulch around the base of the tree rather than grass or flowers.
Remembering the roots is a big part of your tree's health. When someone cuts parts of the roots some of the tree's crown will die.
Having good soil can mean the difference between a healthy and unhealthy tree. A frequent problem is compacted soil from traffic or adding too much soil around the tree. Remember not to place any soil around the tree trunk as this promotes disease and rot.
Improper watering of trees is a common mistake. No rain for 4-5 days can put serious stress on a tree. Make sure to give your trees water during droughts especially on newly planted trees. For mature trees, leave a hose trickling at the base of the tree overnight to saturate the root zone. Young trees require only an hour or two. Regular watering will enhance the healing of wounds and support the growth of new twigs, roots, shoots and callus tissue.
Pruning regularly promotes a healthy tree. This allows healthy branches to get more airflow and have to bear less weight of dead/decaying branches. Removing these branches also helps to prevent disease and rot.