I don't think many would approve of my method, but I rinse my mouth with 3% hydrogen peroxide, I buy it from Amazon.
Though I've never smoked, drank red wine, and always brushed my teeth twice a day I've had yellow teeth as long as I can remember. Laser whitening did practically nothing, and 20% whitening gel in moulded dental trays didn't do much either, I could only eat pale coloured food for a week and my teeth felt bruised.
On American forums I kept reading about how people who couldn't afford expensive treatments used hydrogen peroxide instead. The only thing to remember is that you don't swallow it and rinse with water after.
If I could afford it I would have veneers, but I can't!
I think you would be nuts to use hydrogen peroxide or baking powder at home. Your teeth could end up looking a hell of a lot worse. There is a reason why effective whitening treatments are only supposed to be carried out by dentists.
I had the gel-in-trays thing from my dentist. It worked quite well on my teeth, which were yellow from years of coffee and tea (and smoking, pre-kids). They're not brilliantly white now, but they are a LOT better than they were, and I'm sure they would be whiter still if I had followed the guidelines about only eating and drinking pale foods during treatment (I still drank one cup of tea and one of coffee per day and didn't really change my eating habits )
It did cause sensitivity. Mostly quite low-level, just a constant hint of niggly soreness with the occasional alarming throb of pain. But this all disappeared within 24 hours of stopping treatment, and has been fine since.
It's worth doing for the £300 or so it generally costs. Mine was included in the prices of my braces treatment.
Hydrogen peroxide is the active ingredient in whitening treatments. And 3% is food-grade, a low concentration. It is gradually whitening my teeth, and they are nice and shiny. But you have to keep your tongue out of the way, it can affect the tastebuds and lead to 'furry tongue' in extreme cases!
As a much less extreme example, I have been using Colgate Max One White toothpaste and mouthwash for about a month and have noticed quite a difference. Teeth aren't super-white but do look lighter and brighter.