Hydrogen peroxide is a weak acid used in lots of different ways ; from bleaching paper to hair, and use as a disinfectant and antiseptic.
When mixed with teeth whitening mixtures it becomes a very good bleaching agent and is used used in mouth washes, tooth pastes etc.
In theory it is possible to make your own teeth peroxide mixture at home.
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A mixture of baking soda and hydrogen peroxide forms the most common solution. This can be very easily as the two ingredients of this paste are readily available. You may also want to add a mint flavouring to make it taste better.
However, it's not advisable to do this, due to the risk of getting it wrong and harming yourself. Being acidic in nature, overdoing it can have adverse effects.
So why take the risk. After all, there are many tried & tested home teeth whitening products available, many of which are available on free trials so you can check their results and if they suit you. (Whitening Ultra being once such product)
Remember, that pure white teeth that you sometimes see in the movies is not natural. The natural tooth color is not a pure, snow white, but ivory colored.