I don't know what the practice is in other states, but in Virginia (to the extent of my knowledge) it is done by an overdose of an anesthetic.
I have been present at the deaths of two of my dogs over the years and it is a quick and apparently painless, exit from this life.
Of course, I was greatly aggrieved when they died.
If I make it to those Pearly Gates I will have a question: why did God give us these wonderful creatures but made their stay on Earth so brief?
I've thought that myself over the years.I've felt that terrible loss enough times now to actually thank God they don't live longer.
Seriously. Who else on the planet will love you without bounds and be loyal without conditions and keep your feet warm at night?