Fill a spray bottle with 1 part dishwashing detergent and 4 parts water. Shake the bottle to mix the liquids, and use the soapy solution to kill individual hornets that are well-exposed after finding their way into your home. Thoroughly wet the hornet so the liquid enters his tracheal system, resulting in suffocation.
Mix 1 part water and 4 parts dishwashing detergent in a 5-gallon bucket. Attach a piece of protein, such as liver or fish, to a piece of string and attach this to a wide wire screen that's placed on top of the edge of the bucket. The wire openings in the screen should be wide enough so the hornets can fly through them into the bucket. The bait should hang about 1 inch above the water. Place the water trap in areas where hornets roam, away from human activity. The protein draws the hornets and when they fly down, they get trapped and drown in the soapy water.
Wear a bee suit if you plan on eradicating an entire hornet nest. Alternatively, put on long pants and tie them at your ankles with a piece of string. Also wear a long-sleeved shirt, socks, shoes, gloves and a hat that's covered with netting to protect your eyes and face.
Cover the nest with a large, plastic garbage bag, and cut the nest to release it from the tree. Then quickly seal the bag to trap the hornets. Place it in a sunny area, and the hornets should die in the bag within about two days. Plan on doing this early in the morning or late in the evening when the temperature is cool, and the hornets are less active and have returned to the nest.