I need to write an introduction letter so that I can become a vendor at a festival. How do I do this so that I can sell my cuisine?

I assume that they want your wares (cakes, perchance?) to be unique and desirable.
I would start with a paragraph about how long you have been baking, some accolades or sales figures, and any business/health dept licenses if required and you have them.
Then I would use list format to state what each cake is called, a one-line description, and a price.
I would include one photograph of some cakes arranged on a pretty table setting.
I'd keep all this to one page.
Good luck