To kill hornets nesting in the ground, locate the nest entrance during the day, and wait until dark to pour a powdered insecticide recommended for hornets into the nest entrance. When approaching the nest, move slowly, and wear protective clothing. To avoid startling the hornets, don't shine the flashlight directly into the nest. Hornets are aggressive, so contact a pest control professional if the nests are large or if you're allergic to hornet venom.
Cover the entrance to the nest with soil after the hornets are gone, or treat the nest again in three days if the hornets are still active. If the nest is located in an out-of-the-way area and winter is approaching, avoid the area, and wait until winter begins. Hornets leave their nest when temperatures cool, and the paper-like nest naturally degrades over the winter.
To kill hornets without using pesticides, place a heavy glass cover, such as the lid to a cake plate or a large glass bowl, over the entrance to the hive. Weigh the lid down with a brick, and allow it to remain in place until the hornets are no longer active or for about one week. Use clear glass to allow light to enter the nest, as light prevents hornets from digging an alternate entrance.