I will link to a very good article, it discusses various methods. I do it the same way she does. It may seem unkind, but I tried other recommended methods, and my experiences were similar to those in the article. I use large branch loppers that I keep sharp and are only used for this, nothing else, so they are not dulled. I use an empty vinegar jug hung upside down with rope, with the bottom cut off and the neck cut down til it's just wide enough to get the head and neck through, as my cone. Once you put them in it, they are upside down and tend to calm. Then you can do it and walk away. Any response is the nervous system reaction, it is instant. For me, I found it by far the least risk of error and most humane. The best way to do it over all is always a method that you are comfortable with, that is quick and painless as possible for them. What works for one person may not work for another. I'm sorry you are faced with it, it's never something I like to do, but sadly, a necessary thing at some point. And if you don't have access to a vet that will do it, or that is reasonably priced, then we have to be able to do it. And sometimes circumstances dictate that waiting for a vet appointment can cause undo suffering also. 
https://www.muranochickenfarm.com/2017/06/the-easiest-way-to-cull-chicken.html
https://www.muranochickenfarm.com/2017/06/the-easiest-way-to-cull-chicken.html
