The libGammu library exposes all Gammu functionality for various phones in standard API. It can be used to do anything with your phone, however for easier tasks you might prefer to use Python and python-gammu API.
If you intend to use libGammu in your application, all you should need is to #include <gammu.h> and then use Gammu functions. You can check docs/examples/ for some small example applications. You don’t need real phone for testing, use Dummy Driver instead.
The C API documentation is still more complete in Doxygen format available on Gammu website. This still lacks some parts due to problems in Doxygen - Sphinx bridge.