What is the most effective / cost effective method of teeth whitening?!

So I went to a chemist today and asked the lady who served me what the best method of teeth whitening is, and she recommended not purchasing any of the teeth whitening product that the store had, and that I should brush my teeth twice i each session - The first being with tooth paste, and the second with water and bicarbonate soda... She said this will work just as effectively as any of the products that they sold.

My question is, will this method work, or will it simply dissolve an outer layer of my teeth, and have the same effect brushing my teeth with citric acid will have...

Can anybody recommend the most effective method of teeth whitening? I do not mind paying the $30 every few months, nor do I mind spending the 200 or 300ish dollars every few years... Or, is there a simpler method, such as this bicarbonate soda trick?

Thanks.