In 2012, Vito Tardia published a guide to explore the Dropbox PHP API. The steps to follow include: inform Dropbox about the existent app, code the application, authorization, REST, and Final DropboxClient Object. The author includes a small portion of the code because the full programming source is available on GitHub.
This is older, archived content that may not contain a detailed description of the how-to. Please refer to the URL below for the complete how-to.