Become a student of the fashion show game. A fashion show producer must have an eye for fashion and a working knowledge of critically-acclaimed designer names and what makes them distinctive.
Take business and fashion courses. The business courses will help you handle the unglamorous side of the job. There are no degrees in fashion production, but studying fashion design can only help you produce shows. There are some large fashion-based schools in New York, Paris and some other big cities, but some universities and colleges also offer courses in fashion.
Study how famous fashion show producers got their jobs. Most of them were either stylists, models or designers first, and most of them worked their way into those jobs by assisting an established producer. Intern at fashion shows just to get the experience of working behind the scenes and the chance to observe producers at work.