You can use baking soda and peroxide to get rid of brown spots on your teeth.
Brush your teeth with a baking soda and peroxide solution. Mix the baking soda into a thick paste and apply the paste to a tooth brush.
To keep your teeth clean and prevent further brown spots make sure you brush your teeth after every meal you eat.
Also you might need to use some teeth whitening strips which can help remove brown spots and keep your teeth white but you need to leave them on your teeth for at least 30 minutes for them to be effective.