What is the best way to clean and remove stains from false teeth and bit plate?

The best: Way and what I use in my office and recommend to patients is to purchase powdered dw detergent. Place teeth in a 2 c container that can take boiling water, place 1 tblsp of detergent and add water on the boil. Let sit over night, scrub with a stiff brush (kitchen sink type) then rinse. Repeat as needed.

Many of the : Commercial dental cleaners work well unless contraindicated by the appliance manufacturer. Using any antibacterial soap and a stiff brush to clean the appliances 2x/day typically does a good job. I personally do not recommend using toothpaste as a cleaning medium for dentures, nightguards, splints etc. Those that use toothpaste as the cleaner seem to develop tartar on their appliances.

Brush / soak: I advise all my patients to 1. Scrub them with soft toothbrush or denture brush and toothpaste (brand not important), to remove debris and beginning stain. Then, 2. Soak them for 10 - 15 minutes in an antimicrobial effervescent cleaner -- polident, efferdent, etc. Then rinse thoroughly. If stains stubborn, see the dentist for cleaning and polishing.

Some effort, easy: I would brush away the surfaces of the appliance with a soft brush and a small amount of toothpaste. I would then soak the appliance for at least a few hours in fresh water with a generic denture tablet. That is all that is needed. I would also bring the appliance in with you to your periodic dental visits so that a deeper cleaning may be accomplished.

Most Effective Way: Brush your dentures at least twice daily. Make sure to add some hydrogen peroxide to the bath along with a effervescent tablet. This is the most effective home remedy to clean your dentures.