Over at phpmaster.com they have a great article on how to take advantage of the Dropbox using a third part PHP SDK.
In this article we’ll explore the Dropbox API by building a simple client for accessing files in a Dropbox account. The client will perform some basic operations, such as authentication, listing files, and uploading and downloading files.
To keep the article short and readable, I’ll keep the included code to a minimum and instead refer you to the full code available on PHPMaster’s GitHub. To run the code, you’ll need PHP with cURL support and obviously a Dropbox account.
Your starting point for anything related to development with Dropbox should be the Dropbox Developers Center where you can find the API reference along with its basic concepts and best practices. You can also download the official SDKs, but PHP isn’t listed among the supported languages. There’s a link to a third party PHP SDK on Github.