I know that baking soda can work and whitening toothpaste, but what else which isn't expensive could work for whitening teeth?

Proper toothpaste: Many toothpastes have a whitening agent that does well. This is the way to go!

Avoid staining agent: There are several things that could help for whitening, but you take precautions and it takes longer to see results that a professional whitening: 1-crunchy fruits and vegetables(apples, strawberry), 2-suga free gum xylitol, 3-vinegar and lemon (possible damage of enamel), and most important, avoid staining agents such as coffee, smoking, red wine..

OTC products: There are many over the counter whitening products and strips available for low cost at your local drug store. There are also affordable take home products available from your dentist. Ultradent's tres-white is effective and inexpensive.

Hydrogen peroxide: Hydrogen peroxide is deemed by american dental association to be safe.