the most common euthanasia solution Sodium Pentobarbitol, Butler makes it under the name Socumb. always a fitting name, i thought. overall, it's a very painless way to die, unless your vet isn't very good with injections. if they miss, it burns. i believe it has a ph of anywhere between 7-10, and socumb has alcohol in it to help stabilize it. done right, they just go to sleep.
pentobarbital isn't used so much as a anesthetic anymore, since there are better inhalant anesthetics like isoflurane. inhalants offer you more control of the depth of anesthesia.
it is still used as a anticonvulsant in small animals. i believe there is some large animal use.
i guess pithing small animals and fish is a quick and easy way, but if done wrong is inhumane. but then researchers intentionally pith mice to create situations of paralysis for testing, not to kill them.
when we used to have to care for hawks, we'd have to kill mice to feed the hawks. there is no easy or humane way to kill a mouse that i can share to use it as food for another animal. some of the ways sound heartless, but are actually quick and painless, but look shockingly violent. but then watchin a hawk eat a mouse and listening to it crunch bones like the skull isn't exactly pretty either.
but as far as cats and dogs, if administered right, is painless and quick.