Making your own computer game can be as simple or as complex as you want. Depending on what kind of game you are planning on making, ie console or something more graphical, you could make your own from the ground up. In fact I'm in the process of working with some friends to make my own game engine from where we will eventually build games. (a lone wolf ) We're still learning more and more about OpenGL and C++ (and eventually OpenAL, Networking, and Input).

You don't need to write your own game engine like we're doing, since it takes a lot of time and we've already run into quite a few issues. This is the 3rd or 4th complete restart of the project, in about 2-3 years. This time I am making sure we make everything much more modular than in the past so if it fails, we at least have parts to reuse.

Anyways, for a basic game, Game Maker should be good. He makes a pretty good version avaliable for free, and you get more features such as networking if you register it for $15 (donation system didn't work). I think he teaches something related to gaming at a college to, and that is where is site is located. http://www.cs.uu.nl/people/markov/gmaker/

Also, a good website to visit would be http://www.gamedev.net. Lots of game developer information can be found there, and news. Site layout has somewhat of a learning curve though, but is easy to find as you get used to it. And checking out their headlines, do you want to make a game like Tribes 2? You'd still have to program quite a lot to make a game, but you can get a license to use the engine for $100....