The best option to humanely euthanize a dog would be to have a vet do the euthanize procedure so that the drugs are injected properly and the dog dies a peaceful death.
However there can be an option to and a way to humanely euthanize a dog at home such as by overdosing the dog on some sleeping pills.
The sleeping pills that causes an overdose will eventually cause the dog to pass or you could feed the dog some rat poison in a large enough quantities by adding it the dogs food.
But the rat poison is a slower and more painful death or you have the option of taking your dog out somewhere such as in a rural area and then shooting and killing the dog.
But other than that there's not much else you can do to more humanely euthanize the dog at home.
The actual drugs that are used to euthanize the dog by a vet are highly controlled and are not available for home use.
So the vet would need to administer the euthanize drugs to the dog.
Euthanize procedures for a dog only costs around $50.00 to $100.00 at most so it's not all that expensive and it's the best way to euthanize the dog.