Recently, I gave a lunch-and-learn to my team on the topic of Dependency Injection (DI). Instead of showing a bunch of slides explaining what DI is and what it's good for, I created a small project and demonstrated the process of migrating a codebase that does not use DI to one that does. Each stage of the project is a different tag in the repository. The code can be found on Github: http://github.com/jadell/laldi. Checkout the code, and run composer install. To see the code at each step in the process, run the git checkout command in the header of each section.
He goes through each "checkout" step (the title is the git command to run to follow along) showing how he migrated away from a simple micro-framework based site to one that defines the various objects (and repositories) inside the "application" object. He adds in a few comments to let you know a bit more about what's going on and some basic event handling. He finishes off the post with some potential issues that could come up both during the process and with the resulting application.