How do you remove stains and residue buildup from a toilet?

Judy, I've found that a bleach soak is quite effective. It only takes a small amount of bleach, scrub around the toilet and let sit for a couple of hours. Flush away. Of course, this is for organic stains not mineral stains such as rust or scale. That takes an acid such as vinegar or rust out

I'd try using something like Scrubbing Bubbles and let it sit for an hour or two and then scrub hard. Be sure to keep the area well-ventilated!

Lysol Lime & Rust Remover Toilet Bowl cleaner, comes in a black squirt bottle. Scrub with Scrub Daddy or Mr. Clean Magic Eraser.

Pumice stone and elbow grease