You may be able to become a CAD technician by starting as an apprentice with an engineering or construction firm. See the goengineer website for details about technician apprenticeships in the engineering construction industry.
To get onto an apprenticeship scheme, you may need some GCSEs (A-C), such as maths, science, engineering, design and technology, or equivalent qualifications. However, enthusiasm for the industry is often just as important as qualifications.
An alternative way to gain CAD skills is to take a college course that covers computer design skills, such as: BCS Certificate in 2D Computer Aided Design (ECDL CAD) Level 2; BTEC Certificates and Diplomas in Engineering levels 2 and 3; BTEC National Certificates and Diplomas in Mechanical, Manufacturing or Civil Engineering Level 3; City & Guilds Certificate in Computer Aided Design Parametric Modelling levels 1 to 3; and City & Guilds Certificate in 2D Computer Aided Design (4353) Level 2, and Level 3, which allows you to specialise in 2D or 3D design.
College courses tend to use AutoCAD for learning, which give a good understanding of technical design. Some colleges run more specialised software packages, including AutoCAD LT, Autodesk Architectural, CATIA, PRO/Engineer, SolidWorks and 3D Studio Max.
Check with your local college for exact details of the packages they offer.
See the SEMTA, Engineering Construction Industry Training Board (ECITB) and Women into Science, Engineering and Construction websites for more information.