I tried this one first. It's easy and it works! Use a baby toothbrush to apply it and give your nails a good scrub for a minute or two. You may need to do it several times depending on how stained your nails are. The white colored pasty toothpaste works best as opposed to the blue or green gel-like toothpaste.
Squeeze half of a lemon (or more) into a plastic bowl, and then add and blend baking soda until you get a nice abrasive paste-like texture. Then use an old toothbrush to scrub your nails with it. Rinse, and repeat if needed.
Mix the two together until you've got a paste-like texture. Cover your nails with it and allow the mixture to sit on them for about 3 minutes before rinsing it off with warm water.
Dissolve a couple of tablets in warm water, and soak your nails in it for about 5 minutes. I haven't tried this one because I don't happen to have denture cleaner laying around, but I've heard that it works.
I didn't know this existed until recently! You can pick up a nail whitening pencil on Amazon (maybe even Walmart or Target, too). I like to apply it under the tips of my nails to make them look healthier.
Prevent stained nails from happening in the first place by using a base coat. Duh, right? It's definitely worth the extra step! Don't forget that most of these techniques can dry your hands out, so apply a good moisturizer once you're finished whitening your nails.