Teeth whitening used to be a service that only your dentist could provide. With the advent of at-home do-it-yourself teeth whitening kits and even some homemade recipes this is no longer the case. At your local grocery or drug store you can find multiple formats of teeth whitening tools. There are toothpastes, mouthwashes, press on strips and more.
Most of these kits aren't exactly cheap (I'd say they start at $15.00 but can go much higher than this) so you want to know if they actually work and if they are safe - especially since you are now being allowed to try a technique on your teeth that used to be only performed by a trained and highly educated professional.
The good news is that all of the products you can find in the dental care aisle, to aid in your goal of having whiter teeth, are safe as long as you follow all of the directions. It's possible that if you have sensitive teeth or gums to begin with that these products could cause some discomfort but it should be minimal if you carefully read and follow the directions.
Teeth whitening products are not considered drugs so they are not monitored by the Food and Drug Administration but if a product in the form of toothpaste, mouthwash or gum seeks and qualifies for it, they can have the American Dental Association seal of approval on their packaging. I personally would go with an ADA approved product over a product lacking this certification. If you visit their website, they have an interactive search feature so that you can find ADA approved products. However, the ADA will not endorse over-the-counter teeth whitening kits because, according to their website, "the ADA recommends that if you choose to use a bleaching product, you should only do so after consultation with a dentist. This is especially important for patients with many fillings, crowns, and extremely dark stains. A thorough oral examination, performed by a licensed dentist, is essential to determine if bleaching is an appropriate course of treatment. The dentist and patient together can determine the most appropriate treatment. The dentist may then advise the patient and supervise the use of bleaching agents within the context of a comprehensive, appropriately sequenced treatment plan".
The one at-home teeth whitening kit that they do have listed on their website is Opalescence - "a dentist-controlled, dentist-supervised, take-home bleaching system dispensed in unit dose syringes" so you can't buy it at the store but you can get it from a dentist to take home.
If you think all these products sound too expensive, difficult or chemical-ridden there are also homemade teeth whitening options. One popular, more eco-friendly method is mixing a teaspoon of hydrogen peroxide rated at three percent with a tablespoon of baking soda. To make this mixture taste a little better you can add a dab of essential oils or about a teaspoon of mint flavored mouthwash. If you go with this homemade option, just like all of its over-the-counter counterparts, you wouldn't want to swallow any of it.
Below is a video demonstrating homemade teeth whitening - she says it takes about 2 weeks to see results: