One of the positive aspects of dentures or false teeth is that you can have them made any color you like within reason, so if your own teeth were rather dingy or discolored before, you can switch to bright new ones by having your teeth removed and having dentures. You would not, of course, resort to having all your teeth extracted just for the sake of that, however, since you could undergo a professional in-surgery whitening treatment or even bleach your own teeth at home quite satisfactorily with a good home bleaching kit.
A nice new set of white false teeth doesn't necessarily stay that way for ever, since most false teeth these days are made from acrylic, which is a type of plastic and this can become porous and absorb stains over time. Porcelain teeth are much more resistant to discoloration but are more expensive and are also less forgiving in terms of the "bite" so some people find them difficult to wear if they don't have much of a gum ridge in the lower jaw to sit the denture on. The majority of dentures are made using acrylic teeth which are available in a whole range of shades and are remarkably lifelike.
With dentures you need to clean them daily just as you would with your own natural teeth or else plaque builds up on them and gradually hardens to form calcified tartar or calculus which takes up stains from foods, drinks, and smoking. You can clean dentures best by soaking them overnight in a proprietary denture cleaning solution and then giving them a brush and rinse in the morning. If you have any particularly stubborn stains then it is feasible to soak the dentures in a solution of bleach to improve their appearance. If you did this repeatedly over a long period of time it would tend to gradually remove color from both the false teeth and the artificial gum. This can be somewhat counter-productive in the long term however, because repeated soakings in bleach or an acid solution like vinegar, will tend to make the plastic more porous so that it inevitably collects stains more readily. So, provided your false teeth are the color you want in the first place it is best to keep them that way by careful daily cleansing with a proper denture hygiene product.
As dentures get more porous over time they may also absorb more of the bleach solution which isn't then totally removed by rinsing and might subsequently leach out into the mouth which could be harmful.
If you have been wearing a set of dentures for quite a while and they have accumulated calcified deposits and stains despite your efforts to clean them, then you can take them to your dentist to have them cleaned by an ultrasonic device that uses sound waves to agitate a strong cleaning solution and literally "shake" off the deposits and stains.
If you're having dentures for the first time you can specify whiter teeth but it is wise not to go too far with this since teeth that are absolutely white will look false and draw people's attention. You are much better off to follow your dentist's advice on how much lighter in shade your false teeth can be whilst still looking natural.
If you make it a habit to practice daily cleaning without using any really harsh chemicals or heavy brushing, then you should be able to prevent a build-up of stains and tartar on your dentures, especially if you can refrain from smoking and drinking too much tea or coffee. Do not scrub too hard with a nail brush across the sides of the teeth horizontally, but rather brush the teeth vertically from the gum as if they were natural teeth. This avoids too much abrasion which can otherwise occur and spoil the appearance of the dentures.