First, be sure you have eastern tent caterpillars, and not another similar pest. Eastern tent caterpillars build their tents in the crotches of tree branches and appear in early spring. Fall webworms also build tents, but their tents will be at the ends of branches, enclosing foliage. Fall webworms also appear at an entirely different time of year - fall, as you can probably guess. Some people confuse eastern tent caterpillars with gypsy moths. Gypsy moths do not construct tents, and usually appear a little later in spring than tent caterpillars.
Eastern tent caterpillars rarely infest ornamental trees in large enough numbers to kill your landscape plants. Because they appear in early spring and complete their life cycle by summer, the host trees have time to produce more leaves after being defoliated. If you have a few caterpillar tents in an apple or cherry tree, don't panic. Control of the pests may not be necessary at all. If the infestation is significant or you just can't stand the sight of caterpillar tents in your trees, there are some things you can do:
Mechanical controls - Remove the caterpillars by hand. The caterpillars will rest inside their tent after they feed. When you see a large group of caterpillars in the tent, use a stick or gloved hands to pull the tent from the branches, caterpillars and all. For a large tent, you can wind the silk around a stick as you pull it from the tree. You can crush the caterpillars or drop them in a pan of soapy water. In the fall, once leaves have fallen, look for egg masses on twigs of the host trees. Prune out any you find, or scrape them from the branch and destroy them.
Biological controls - Young larvae may be treated with Bacillus thuringiensis var kurstaki, or Bt. Bt is a naturally occurring bacteria that interferes with the caterpillar's ability to digest food. It must be applied to the foliage of the infested trees. The caterpillars ingest Bt as they eat, and will stop eating immediately and die within a few days. You do not need to spray the tents or the caterpillars. Late instar caterpillars, especially those that are already migrating to pupate, cannot be treated effectively with Bt.
Chemical controls - Some contact or ingestion pesticides work on eastern tent caterpillars. If you feel the infestation requires this drastic an intervention, contact a pest control specialist in your area.
In the past, people would burn the caterpillar tents. This probably does more harm to the tree than the caterpillars, and the practice is not recommended.