More than one way...

Q: What is the best and most humane way to kill a cat oneself?

A: Poison is the most humane way to kill a cat. It will just fall asleep and never wake up.

But if you're going to kill a cat, my advice would be to have some fun with it. Perform experiments on it, like seeing how long you can keep it alive in a water tank. Feed it asprin until it's head explodes. Stuff it with fish biscuits and kick it in the guts.

Poison is boring.