Answer:
The most humane way to euthanize a dog is by overdosing with sodium pentothal or sodium brevitol. The animal will painlessly drift off to sleep.
Euthanizing or putting your dog to sleep-is not a "do it at home" sort of deal. This sort of thing must be done at either the local animal shelter or by a licensed vet. They simply inject the dog with Euthanasia and it shuts down their muscles, causing a painless death. It is pain free and they go peacefully.