Munku: Sorry to hear about your pet.
I've never personally had to put a pet down, though a few of my family pets when I was younger were euthanized when they got too sick to keep on. The local animal shelter should be able to help financially, though I'd make sure that they're employing humane methods (injections as opposed to gassing).
If the pain is only because of age and not a result of a terminal illness your vet may be able to prescribe something stronger than aspirin that would allow your pet to live out it's natural life pain-free without hampering it's quality of living.
Locobot: In rural areas, that's actually pretty common. Not because all West Virginians (or southerners or rural people) are sick weirdos, but because for some people, that is a more economically and emotionally suitable method. I don't personally partake or believe in it, but it doesn't mean that I'd mock those who do as being hillbillies or mountain-dwelling sodomites.
For some people, it's almost like a form of personal responsibility: having been the person to care for the pet in life, certain individuals feel that it's their burden to take the animal out of this world as quickly and painlessly as possible (a bullet is much more humane that gas euthanasia).
(FYI, "Deliverance" was set in Georgia, not West Virginia)