The brown spots on the teeth are most probably stains or tartar. The stains could have come from food, cigarettes, caffeine or many other sources. First try brushing regularly for a few months, also switch toothpastes. If this does not work then you'll probably have to go to a dentist to get the stains off.
A dentist could polish your teeth. If the stains are light then the dentist will use a bristle cup with a particular paste and rub your teeth with a circular motion, the brush could be mechanized. He could also bleach your teeth by oxidizing it. This should not be done often as it could make the teeth brittle. If the stains are dark then he could apply a thin coat of ceramic to the teeth, this technique is called bonding. If the teeth are beyond repair then the dentist will slowly erode a significant portion of the teeth with a fast rotating instrument. He will then fill the gap with a ceramic crown.
A dentist could polish your teeth. If the stains are light then the dentist will use a bristle cup with a particular paste and rub your teeth with a circular motion, the brush could be mechanized. He could also bleach your teeth by oxidizing it. This should not be done often as it could make the teeth brittle. If the stains are dark then he could apply a thin coat of ceramic to the teeth, this technique is called bonding. If the teeth are beyond repair then the dentist will slowly erode a significant portion of the teeth with a fast rotating instrument. He will then fill the gap with a ceramic crown.