If you’ve set up your Info.plist’s CFBundleDocumentTypes array properly (either ‘LSItemContentTypes’ or ‘CFBundleTypeExtensions’), then you just need to set up an NSApplication delegate and implement the delegate method, application:openFile:.
If you’re expecting multiple files to be dropped at once, implement application:openFiles:.
For promised files (NSFilesPromisePboardType
/kPasteboardTypeFileURLPromise
) see Dropping promised files on to application icon in Dock.