Is there an inexpensive way to fix stained/discolored teeth?

Yes : Sadly -at the end of the day you get what you pay for. Composite veneers are cheaper than porcelain / ceramic veneers. Teeth whitening and micro air abrasion might be an option - also using mi paste. Most important to have your expectations realistic. Best to see a dentist for a work up and treatment options.

Whitening toothpaste: Use a whitening toothpaste, they are usually abrasive and remove staining to a point.