There are lots of different places that you can start.

I think the best thing to do if you are a true beginner at game programming is to research what graphics, sound and input libraries you'd want to use. You can then look at demos and samples from the various ones and see which you prefer for whatever your reasons.

For FPC specific support, I'd recommend JEDI-SDL as I use it myself. The Phoenix library is supposed to be quite good too. You could try your hand at using the OpenGL and DirectX headers, but those can be a bit much for a beginner to start with.

OpenAL headers for sound are actually surprisingly easy to use --I find-- if you have a few good demos to see how it is setup. Though a quick understanding of 3D audio can help figure things out too.

There are other things, but those would be the best for FPC out of the box.

Also, if you wanted to learn how to make a simple game to start there is my tutorial series, aimed at beginners, in the Articles section of PGD. I use Lazarus and the JEDI-SDL library to keep things simple and provide all the sources so it is easy to follow.

Feel free to check it out; Artillery Game Tutorial