To avoid tooth sensitivity and the abrasiveness of other methods just do oil pulling. Swishing coconut oil in your mouth for 10-20 minutes with a little peppermint essential oil and you'll have white teeth. It's inexpensive. Just don't spit it out in your sink because it will clog your pipes (and ruin your septic system) spit out it out the garbage. Also, never swallow it. It's meant to detoxify the mouth, by getting rid of bacteria. And it certainly helps with regard to gum health.
There's also charcoal but I'm not a fan.
There's also charcoal but I'm not a fan.