Composerizing a non-composerized Drupal site to a Composerized Drupal site

1. “Composer is a dependency manager tool for PHP.” This means that we can easily manage php libraries and their dependencies using Composer.
2. In terms of Drupal, we can download and manage Drupal core, contributed profiles, modules, themes and libraries using Composer. In fact, the entire project can also be managed using Composer.
3. Using Composer is the modern way to work in PHP as modern frameworks utilize Composer to manage their dependencies, and it is nice that we can do the same in Drupal.
4. Composer also gives us the ability to autoload PHP classes thus making code easier to read and write.

How do we shift from Non-Composer managed website to Composer managed website?