Spray a wasp and hornet spray into the entrance of an exposed nest during the evening, when wasps are least likely to be flying around. Observe the nest over the next three days, to determine if there is any wasp activity.
Repeat the treatment at three-day intervals, if you continue to observe activity, until all the wasps are dead.
Treat small, exposed nests by sealing a plastic bag over them, in the evening, and cutting the nest off from the tree. Either freeze the bag or allow it to sit in the sun; the wasps inside should be dead within a day or two.
Pour a solution of dish soap and water into the entrance of the nest.
Observe the nest for the next few days to detect wasp activity. Treat the nest, if you still observe activity, with an insecticide containing carbaryl or chlorpyrifos as a dust, or carbaryl, diazinon, or acephate as a liquid concentrate. Make sure that you use an insecticide cleared for ground use.
Cover the nest with soil after treating.
Drill small, 1/8-inch holes in the wall, to give you access to the void in which the wasp nest is located.
Use a small amount of insecticidal dust, containing bendiocarb, chlorpyrifos or boric acid, to treat concealed nests in the void. Make sure that your insecticide is safe for home use. "Puff" the insecticidal dust into the void, either using the applicator provided with your insecticide or an empty liquid-detergent bottle.
If your treatment is ineffective, consider hiring an experienced pest control service to exterminate the wasp nest.