How can you fix stained/discolored teeth inexpensively safely?

See a Dentist. Often home remedies cause much more harm than improvement. Your dentist can evaluate the stain/discoloration & determine if can be safely lightened, or determine if it is decay that needs to be treated to prevent deepening, if left untreated, decay will dramatically increase in size, causing pain & need for root canal treatment. Even if you are on a budget, your dentist can help you.
Ortho phosphoric aci. Superphosphozyme by biotics will whiten teeth. Use a qtip with few drops use on teeth and rinse off using water with little baking soda to remove any acid (or just rinse thoroughly).
Be careful! It's never smart to try otc products without consulting a professional first! i also hope that you are not one of those individuals that care more about "white" teeth than "healthy" teeth. Ask your dentist what can be used within your budget. There are several effective relatively low cost products although they may not provide the best results.