To get started with using the Box API in PHP, developers need to create an application on the Box developer portal, grab the PHP helper library, and make minor edits to upload it to their server. They then use the library to authenticate with Box, retrieve the file tree, and add comments to a file by SMS through Twilio. The code examples provide a basic structure for interacting with the Box API, but note that they lack additional features such as storing authentication tokens securely and providing user-friendly interfaces. Once set up, developers can build their own applications using Twilio and Box to comment on files through SMS.