The author sets up a local development environment using Chef Development Kit (DK) version 0.15.15 to test a Chef cookbook, specifically the `chef-selenium` default recipe. They use ChefSpec, a unit testing framework for testing Chef cookbooks, to simulate the convergence of resources and prove that the cookbook code works correctly before pushing changes to production. The author writes tests for various scenarios, including installing and uninstalling packages on different platforms, and verifies that the tests pass using Rake. However, they note that the test coverage is not 100% due to missing tests in some recipes, and provide a snippet of code to enable test coverage for future improvements.