Setting up a local debugging environment for serverless applications using the AWS SAM CLI involves installing and configuring essential tools such as the AWS CLI, Docker, and VSCode. The SAM CLI, a Python-based command-line tool, facilitates the creation and management of serverless backends by emulating the AWS Lambda cloud environment on local machines using Docker. Developers can initiate a SAM project, write and test Lambda functions, and utilize VSCode's debug UI to set breakpoints and inspect variables. By configuring a launch file in VSCode, users can connect to the SAM CLI's debug process for a seamless debugging experience. Additionally, developers can streamline testing workflows with NPM scripts, allowing for efficient invocation of functions in debug mode. This setup aids in effectively testing and debugging serverless applications, ensuring they closely mimic the cloud environment where they will ultimately be deployed.