Game designing/development is a long and complex process from concept to completion. It is a team job and involves designers, programmers, artists, writers, project managers, animators, audio engineer, testers, and others.
As a game designer, one should be creative and imaginative, have excellent communication and technical skills, knowledge of various game platforms and technologies, and be able to work with teams.
In short, you should have software knowledge and other technical and professional skills. Though not compulsory, but formal education can help get the knowledge and skills, understand game development process and prepare for a successful career.
You can join a game designing/ development or other related course offered by any well-known good institute.
Or specialise in a field you like most such as programming, animation, arts/designing, computer science, sound, etc. and then enter gaming industry or any other industry within that capacity.
Make a portfolio of your work and get on-the-job training experience or start as a game tester.
[Answered on September 19, 2014]