There is no one process that every game designer follows, though there are a number of things you can do to achieve such a career. One way to become a game designer is to go to school specifically for that purpose. A degree in game design may help you land a job in the field, and you will learn many necessary skills. The other way is to work your way through the system, and many game designers begin as programmers or artists. If you are not interested in either code or art, you may be able to become a game designer if you start in quality assurance (QA) and work your way up.
A number of colleges and universities offer four year degrees in game design. Specialized vocational schools that cater to the video game industry also offer programs to help you become a game designer. You will often learn about various management skills in addition to principles of game design, since a designer can be the head of a project team.
Most companies don't hire game designers straight out of school, so it can help to have another skill that is useful to the video game industry. Many programmers, artists, musicians, and other development staffers eventually move into game design. Sometimes the best way to get your foot in the door to eventually become a game designer is to hone your expertise in one of these fields. Some schools offer programming or art degrees with a game design focus, which can help you with the specific knowledge and experience you will need to work in the industry.
Another way to become a game designer is to create your own simple games. Many successful game designers started very small, creating all of the code and art for their own games. There are a number of specialized programming languages, libraries, and frameworks that can help a new game designer prototype and create his first game. If you have actual working games in your portfolio, that can go a long way towards helping you become a game designer.
Quality assurance is another way that many people first get started in the industry. These jobs often involve monotonous bug testing, though highly skilled and motivated people will tend to learn about many aspects of game development. Starting out in QA can sometimes lead to a career in management or even game design positions.