I dyed my hair dark brown underneath about 3 months ago and it hasn't really faded and I really want to go to a light brown red but I don't know if it would work or not. So how could I do it cheaply at home?

I did it myself with Naturtint it is a colorant without ammonia and can lighten your hair up to 2 shades. Just type in your search engine Naturtint color chart and if you like their red Vitacost has the best deals they have also a number where you can call for advice .
Make sure you do a strand test before applying the color all over you head. You may have to mix 2 colors to get the result you want or not.
Good luck