You will need a high level of design skill and creative vision.
You would normally start as an art department trainee/runner in film and TV. You could then work your way up to designer as you develop experience and contacts in the industry.
In practice, many set designers have an art-based BTEC HND or degree. Several universities, colleges and drama schools offer specialised courses in theatre design, performing arts (production) or design for film and television.
Other useful subjects include interior design, fine art, 3-D design and architecture. You should check with colleges or universities for course entry requirements.
Whatever your qualifications, you should find practical work experience and build a portfolio or 'showreel' DVD of your design work to show to potential employers.
You could get relevant experience through getting involved with activities such as student film or low-budget independent films.
You may be able to start in the film and TV industry through an apprenticeship-style new entrant training scheme, such as the BBC's Design Training Scheme. Competition for places on this type of scheme is very strong, so you should still gain practical experience as explained above before applying.