To become a costume designer you will need a high level of design skill and creative vision, as well as practical sewing skills.
In practice, many costume designers have a BTEC HND, degree or postgraduate qualification in costume design, fashion, theatre design or performing arts (production). To find a suitable course, use the course search on this site and check with colleges or universities for exact entry requirements.
Alternatively, you could start as a wardrobe assistant or costume maker and work your way up to designer as you build experience and contacts in the industry.
Whatever your qualifications, you should find practical work experience and build a good portfolio or 'showreel' DVD of your design work to show to potential employers.
You can get relevant experience through student theatre and film productions, amateur theatre, working as a costume ‘daily’ (a temporary helper) on TV or film sets, casual wardrobe work in theatres and working for a theatrical costume hire company.