The quickest and most eficient way would be to have them professionally whitened by a dentist.
If you can't afford that the next best thing is to use whitening trays or whitening lights on your teeth. For the fastest results be sure to read the boxes and find the kits that offer whitter teeth in 1-3 uses...not the one's you use for months.
Whitening your teeth is an ongoing process though. You can't just whiten them once and be done. You have to keep up with the upkeep by using whitening toothpaste and wash daily when brushing your teeth and periodically whitening them with the kits again once they've started to stain again.
Crest whitening strips work pretty good & fast. Each time you use one, you can notice your teeth become increasingly whiter. The only downside that I can think of is that if your teeth are sensitive, it might hurt a little, but that's really it. Anyway, you can get it at like Target and Walmart and places like that if you're interested. You could also get crest whitening tooth paste as well as the strips, which will probably speed up the process using both. Goodluck :)
I try this sometimes. I take peroxide and mix it with water, salt, and baking soda.. The peroxide can do it without the other ingredients but, to be safe of not swallowing it just add them :D
Baking soda....it is cheap and easy no instructions or waiting required. Just dip toothbrush in add ur favorite toothpaste and tada whiter teeth.... never diss the old school methods.