How can I drop a file(or select to open it in Finder) of a type specified in the Info.plist onto my dock icon and then calling a method with the full path of the file?
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:.
If you're actually making a document-based app, setting it up to give you the path will have you doing far more work than you need to. Simply use the document-based application template. The document controller will create an instance of the right class for you; you need only write that class.
An application you create this way will handle file drops (by opening them as documents) for free.
Select your application in the target group of the side pane and use get info. Then in the new window select the properties tab to add a new document type. Name it "Folder" for convenience and the OS Types needs to be "fold"; the store type and role you can leave as is.