Hello thr, i feel you need to visit dentist first to evaluate.sometimes stains are due to food accumulation such as calculus n yellow stains or due to other habits. Then plan treatment accordingly,  scaling and polishing is necessary and followed by bleaching if needs then only.

Yes you can buy Home Teeth Whitening Kit. On a regular basis one can use "Colgate Total" It has multiple ingredients to prevent common dental problems.

Brushing at night regularly and rinses after brushing with Hydroxyl mouth wash ( it is a mild bleaching agent) helps in making tooth shade better . Eat more of fibrous and coarse diet ( fruits like apple , pear, green guava) less of sticky foods like pasta and bread and chocolates

Teeth whitening cannot be done at home. Nor should it be done. If your teeth are having a layer of debris due to food accumulation. It can be cleaned by scaling and polishing of your teeth. Permanent yellowishness due to fluorosis or natural tooth color, those can be corrected by getting porcelain veneers or crowns or composites.