Dropbox offers native SDKs for iOS, OS X and Android. This page includes instructions on how to download and set up SDKs for each platform, as well as links to SDKs provided by the community for other environments.
Before building an app using the Sync API, you'll need to create an app with the App folder or File type permission in the App Console (Full Dropbox permission is not supported with the Sync API). Visit the developer guide for more information on the different types of permissions.
Xcode 5 or later with the OS X development kit is required to build an OS X app using the Sync API. The Sync API requires OS X 10.7 or later.
Once you've downloaded the Sync API OS X SDK, you'll need to add the framework to your project.
Now you want to make sure that the framework will be copied into your app bundle.
If you want to see the Sync API in action, check out the Examples directory in the SDK bundle. There you can find a simple note-taking app that uses the Sync API to save notes to Dropbox and alerts you if the notes are updated. This app will also sync notes with the notes example included in the SDKs for other platforms.