What Can I Use At Home To Euthanize A Cat Who Is Sick And Lost A Lot Of Weight And Cannot Function Properly?

Ooh, buddy, do you really want to traumatize yourself by murdering your cat?? I know it's for a greater cause than letting it die slowly, and i'm sure in this economic time you're strapped for cash. But ASPCA regulations would strongly disagree with your course of action and suggest bringing it to a vet, or even a humane society to have it put down.
Unless you have access to the exact same instruments and chemicals used by licensed professionals, and have an actual permit/degree/license etc stating that you know how to and are authorized to properly euthanize an animal for humane purposes, this is something that most definitely would NOT fall under a "Do-It-Yourself" "Home Remedy" category.
Technically, any poison to humans would be a poison to cats, but the tremendous guilt of performing the action and watching your life-long friend die in front of your eyes is the worst thing you could possibly experience.
Take it to a pound. End of discussion.