Well, there is no one way to go about making a game, of course. Many factors come into play, and here we'll only cover some of the more general principles.
Game design is always an iterative process, where you constantly develop, test and revise. A core component in this process is rapid prototyping, where you build prototypes of your game and continously test this prototype. Is it fun to play? Does the core mechanics work?
Some of the phases and areas to consider:
Business models
How are you going to make money on your game? Are people paying up front, or do you plan to sell items or services within or around the game? These are important questions, and should be considered right from the outset (see also "How do I... Create a good business model").
Target audience
Who would you like to play your game? It's not always easy to figure out, and often you'll probably find that unexpected groups of people are playing your games. Even so, you should consider defining and researching your target audience, as it holds certain implications for the game design, distribution channels, business models etc.
Ideas
How do you go about generating ideas? The romantic idea of full-fledged ideas just appearing in the minds of truly creative people is the rare exception. On the contrary, the initial idea itself is rarely particularly good, and therefore needs to be revised and refined. Don't expect your idea to be "finished", but a constant work in progress. Don't accept the first idea, but be critical and always look for better solutions.
Development
The actual development phase takes on many different shapes and sizes depending on the type and scope of game, the platform you're developing for, the production values etc.
It is important to maintain focus on what it is you want to achieve, and to keep testing if your idea of the game aligns with people's experiences playing it. Focus on what is most important to reach your desired play experience, and don't ever be afraid to cut features and/or reduce the scope. Also, don't be afraid to ask for help, as most people in the games industry are typically keen to assist and contribute with both technical insight and creative ideas.
Promotion & marketing
Making a great game is no guarantee for commercial success. You need to build awareness of the game to attract attention from your potential players. This can be done via more traditional channels such as commercials, advertising, game trailers etc, but we're also seeing an increasing focus on game developers participating in online forums, on Twitter and so on.
Even more important than promoting your individual games is building a community around your company. In the long term, the more people you have interested in your body of work, the more happy (and paying) customers you have. Be relevant, provide value and interact with the community in a positive and constructive way. Those who do this well are securing a solid foundation for themselves, which might make further promotional activities redundant.
Post mortem
A post mortem is the game industry's way of analyzing and evaluating a game once it's been launched. In order to learn from the process, this can be a valuable way of identifying what went well and what needs revision in the next game development process.