There is no cheap way, if it's cheap, it won't work, or at least won't work well. The only sure way to get them whiter, apart from brushing regularly and avoiding things like coffee that stain, is to go to the dentist and have them bleached. I know this because my dad is a dentist.
Better get checked yourself at dentist n ask for the treatment coz sometime teeth discolouration may be natural or artificial. .. If it's natural n colour change is of biological than no topical treatment will solve it n if it's artificial or topical stains than easy treatment are their to make it whiter. ... Don't use soda or any acidic medium ti whiten your teeth coz it will erode your topical layer of teeth n later it will give u rough n sensitive teeth