I mentally start distancing myself from them, I don't watch them or talk to them.
It will really help to have some moral support, does not need anymore experience than you, you can watch you tube. But just someone to do it with you. I have found the upside down in a cone, and slitting the neck just works the easiest with me. I have caught them with a fish net, and slit their throats through the net if they were pretty mean and hard to handle. Do not be surprised if you get the nervous giggles, it happens. Once they are gone, the processing is easy. Once the feathers are off, looks just like a chicken at the store.
Animal husbandry is about choosing who stays and who goes. Some birds do not fit in the set up, and once you get it done, it is so much better for the flock. You do not have to nor should keep every bird. To me the forever friend does not apply to chickens. I keep a flock, the birds in the flock change over time and need.
That being said, knowing I have dispatched many.... also know that I need to do three and I don't even have a plan as to when to do it yet. It is not easy, but it is doable.
Mrs K