Glad you asked...
For a quick and painless death, you could take the dog outside and shoot it. But that's not an appropriate way to put a dog down. To be humane, you should take your dog to the vet and let the vet administer a euthanasia solution. It is very quick, it's painless, it's inexpensive and you don't have to participate.
oyork     How-To Expert
Then again, this answer might help you...
Although, I can certainly understand your reasoning for wnatinf to do so, it is really better to to this in a vet's office or at your local shelter. You can always stay with your dog, and you know it will be done in the proper manner.
Dareth     How-To Expert
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