In reality, we can't all have perfect, shiny white teeth. Fortunately Photoshop was basically designed to break the bounds of reality, letting you do whatever you'd like, but let's be a bit more humble and just learn to whiten some teeth.
Photo by esperales
The process is fairly simple, as demonstrated in the video above. To white teeth you simple need to desaturate the yellow-ish areas and then bright them up.
First, take the Sponge Tool and paint away the yellow parts of the teeth. You can use the default settings (desaturate, 50% flow) but you'll want to pick a brush size that'll fit nicely into the teeth you're whitening. Desaturating with the sponge is going to leave you with some ugly grey shadows, unfortunately, since yellow is darker in tone than pure white. But we can fix that! In the same place you found the sponge tool, you can also select the Dodge Tool. This tool will brighten up areas of a photo, but the default flow setting (50%) is way too high. Something between 10-15% will work much better. You also want to make sure you dodge tool is set to brighten up the midtones, which you can select directly to the left of the flow settings. Once you've got that all set, you can easily brighten up the shadows a bit so the teeth look more naturally white. Don't overdo it, however, otherwise they'll look too perfect and therefore fake. It's important to leave imperfections.
That's it, you're done! This is just one way to whiten teeth, but I find it to be the fastest and the most effective. If you have another way that you like, please share it in the comments.