Change the location of annual plants from year to year to disrupt the life cycle of pests. Remove infested plant material from the garden in the fall. Hain recommends getting rid of the tomato hornworm this way. Other methods are hosing down plants to dislodge insects and pruning diseased or insect-infested woody plants such as raspberries and roses. One can provide barriers, such as row covers, to prevent insects from laying eggs on plants.
Insect traps are also available.
These applied approaches include introducing natural enemies of pests into the garden and improving their effectiveness by creating a favorable environment for them. But before any of this works, the gardener has to become at least somewhat adept at identifying bugs, both the pests and their natural enemies. If there are children in the family, they may enjoy insect identification as part of the gardening experience. Some are available commercially. It's helpful to include plants in the landscape that attract beneficial insects.