DrupalX's magic mainly relies on two pillars: First, the numerous extensions to the Twig template language. Second, a comprehensive API that can be called from PHP and Twig alike. On top of that there is some glue and fixes (like additional hooks, small Drupal bugfixes etc.), to make everything work as intended and to help you through all the common pitfalls you usually encounter when trying to build real-life websites.
DrupalX makes use of Twig's extensibility features to upgrade it to a full object-oriented language geared towards output creation and manipulation. DrupalX will make it easy to have your Drupal content (nodes, menus, forms) rendered anyway you want and anywhere you want.
So, to dive right in you should perhaps first get acquainted with DrupalX's key concepts. Next, find out how exactly DrupalX extends the Twig language. And, finally, see our class library (API) documentation to find out everything you can do with DrupalX. You'll find everything right on the home page - or, for the lazier ones, we link it right here:
Key concepts Twig extensions Class library (API)