You will need a high level of design skill and creative vision.
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 drama groups.