That question is too broad to answer - it is effectively unanswerable because, like most code and application development, it all depends. Generally professional WordPress development (creating your own code to implement functionality) happens through programmers using a code editor/IDE to develop plugins using standard computer science and engineering methodology on top of WordPress' flexible API. At a high level, it's just like development for any other application in any other language.
All that being said, I will point you to the WordPress codex here and the WordPress code reference here. Read through the codex to get an idea of how WordPress architecturally works and then use the developer code reference to delve into the actual functions, classes, methods and hooks used by WordPress.
Also I recommend opening up the WordPress core PHP files in your PHP/text editor of choice and read through the code which is generally very well documented. Don't actually edit these files though - it's always bad practice to edit the core files as they will get overwritten in WordPress updates and you'll lose your changes. Instead make any customizations through a custom plugins or custom themes.