Most practicing game developers are part-time game developers, meaning they devote only part of their time to the development of games. Although game developers usually are associated with programmer types, there are many other roles in the game development process: game designer, graphical artist, writer, sound designer, music compositor, and other, similar roles.
By far, game designer is the most sought-after role, because most people assume this is the easiest way to get into the industry. After all, what can there be to designing a game? A lot, and many companies will require you have serious communication, theatric, and other skills before you can land this position. In addition, some companies require you have a B.S. in Computer Science.
The artistic position requires artistic experience. Not just anyone can be an artist, especially a good artist, which is required for computer games, which often have color and resolution restrictions. Still, if you have skills in this area, this is a good position. Many companies will ask you for a portfolio of your work, which you should not send electronically. Large companies tend to respond better to snail-mail than e-mail, and will not even look at submissions e-mailed to them.
Like the other positions, being a writer requires some training, and, of course, a solid dose of imagination. Writers are often called to write scripts, character dialogue, and, in the case of technical writers, online help and printed manuals. This is a position best suited for contract work, as few game companies have need for a full-time writer.
And last but not least, there is the software developer position. This is, by far, the most flexible position to take. You can find game development jobs that do not require a B.S. in Computer Science, or even do consultant work if you are experienced. Best of all, there is so many resources for programmers that almost anyone can pick up the skills with a year or two of light work. Companies usually want some samples of your work before they will consider hiring you. Make them polished, well-made programs that illustrate your strengths.
If you are not interested in working at a company, you might be considering part-time work. You could, for example, become any one of the aforementioned types of game developers and form a small team of people willing to create a game without advance funding. This has been done quite often and successfully in the past, providing all parties have taken appropriate legal protection.
In any case, you need resources. If you want to become a programmer, you'll need some good books on programming, a compiler, and game development books. The language to learn for programmers is C++, and then possibly Java (if you intend on doing Web-based games). Pick up any Teach Yourself C++ In 21 Days book, an advanced C++ book, and a couple of good game programming books (one of which should be my CUTTING EDGE 3-D GAME PROGRAMMING WITH C++ book, should you intend to pursue 3-D game programming).
If you want to become an artist, start taking art classes! You'll need a good paint program and a 3-D modeling program. I recommend Paint Shop Pro for the first and a low-cost modeler such as TrueSpace for the second. These tools will enable you to get started in the industry, but plan on eventually buying a more advanced (and more expensive) paint program and the modeler 3DS MAX for serious game development.
If you have writing skills, then you're all set for the writing position. Otherwise, read lots of fiction and study the English language -- it will pay off, believe me. Then create some sample scripts and story-lines and try to get them into game form. If you succeed, you're set for life.
Game designers need experience laying out levels, so if you want to become one, note carefully the structure of levels and environments in top-selling games. Take theater, communication, and computer science classes if you are looking to land a good position at a large game company.
Once you get into the game industry, you won't be able to get out. It's constantly changing, very addictive, and is almost as challenging as it is rewarding. Good luck!