Getting rid of hornets isn't much different from getting rid of yellow jackets. Here in the United States the most common hornet, the Bald-faced Hornet, isn't actually a hornet at all, and is more closely related to the Yellow Jacket wasp. The primary differences between the yellow jacket and the hornet are size (the hornet is larger), coloring (hornets are ivory and black), and hunting behavior. The real reason the bald-faced hornet is referred to as a hornet because it builds an aerial nest, while yellow jackets prefer to build nests underground—usually in abandoned rodent burrows.
While yellow jackets are big fans of sugary treats like soda and syrups, hornets tend to restrict their diets to live prey—insects mostly. Because hornets prefer hunting live prey, their contact with humans is minimized. Generally speaking hornets only attack other creatures (like you) if their nest is disturbed, and if this is the case they will mobilize the entire colony in to defend the nest—a potentially life threatening scenario for some people. Below, I will describe some preventative, non-chemical ways to get rid of hornets as well as ways to kill hornets and hornet nest removal.
Practical Non-Chemical Hornet Control
Hornets prefer protein and will eat meat and high protein substances like pet food. It is best to keep such things as fish remains, pet food, and other sources of protein out of your yard. This can include compost piles and compost heaps where raw fruits and other protein rich materials are left out in the open. Try to keep compost heaps either buried or kept in sealable containers. Keep pet food in sealable containers if you have outdoors pets, or if you can get pet-released food containers, that will work too.
Keeping garbage cans sealed, clean, and taking garbage out regularly should help get rid of hornets. Even though hornets do prefer to feed on other pests, there are times when food is scarce and grabbing a bite to eat at the local dumpster is just easier. Garbage cans that are left outdoors should have a spring mechanism to keep them closed. Garbage bins should have a top that seals properly and is never left open during the early months of summer (while hornet nests are still growing). If you can't manage to keep garbage sealed, you may want to think about dusting what garbage cans you have with Borax now and again.
Vinegar apparently makes a good bait for water traps designed to capture and get rid of hornets. A company named Skone has designed something of an adaptation from the original do-it-yourself 2-liter soda bottle wasp traps. They still use a 2-liter or even a 1-liter soda bottle (so long as it has a standard mouth, not a "wide" mouth), but what they've done is created an attachment that simply fits onto a bottle, so there's no cutting involved. Very smart. Just add 1 cup of sweetened water (sugar only), one cup of apple cider vinegar, a drop of mild dish soap, and some raw meat for the hornets, and you're ready to kill some hornets.
There is another type of non-chemical trap that is useful for getting rid of hornets, and it's called a Queen trap. Now, because queen hornets are solitary creatures in the early spring, looking for food and a good place to nest, it would follow logically that you could stop the entire process of colony building if you caught that one wasp. This is what queen traps are for. Any kind of homemade trap will do, but the key is to get a piece of raw meat out in the open early enough in the season to gain the attention of recently awoken hornet queens. Kill the queen, and you've essentially spared yourself and your neighbors the trouble of spraying your yard with nasty chemicals.
Mechanical extermination outdoors is not a recommended means of getting rid of hornets, but it is a good way to get rid of hornets indoors. When hornets are killed, a hormone is released that triggers nearby hornets to attack. It's a safety mechanism, designed to keep the nest safe from intruders. Rolling up a newspaper and swatting a hornet outside is what we call "signing your death warrant," especially if it's remains are smeared all of over your pants or something. For those hornets who manage to get indoors, simply vacuum them up and in a matter of days they should die of starvation or dehydration if they've managed to survived being sucked through a vacuum in the first place.
Hornet Nest Removal
Hornet nest removal isn't any different than wasp nest removal, except that you won't have to worry about underground nests. Hornets differentiate themselves from their yellow jacket cousins by building aerial nests. The problem is getting the poison up there. Thankfully, the companies who make products like Raid have a special kind of hornet & wasp killer that will project a spray up to 15 feet into the air. You'll want to do this at night, wearing protective clothing, and you want to make sure that you get that spray directly into the entrance usually found near the bottom of the nest. Try not to break the tissue like construction of the nest because if you do, and the hornets are mad, you'll have a bunch of angry hornets scattering this way and that. This isn't necessarily a problem because most sprays kill hornets on contact, so the ones who do escape are probably about to die. If they don't, well, that's what the protective clothing and the running shoes are for. Oh, did I forget the part about running shoes?