How do I completely uninstall an app in OS X without the use of a dedicated app eg AppZapper?
In general most programs place files within the App icon, which is really a special folder for the Applications files. Many also add files within the Application Support folder within your library. 

Simply drag the Application icon to the trash, and empty it. Then open your Library folder (you might have to click on the "Go" menu item in Finder, while also holding down he Option key to expose the Library). Look under the Application Support folder, and see if your Application has a folder, which you may also trash. You can also do a general search in this folder for the App name or Software company name.

Of course some apps also put other files in other places, such as LaunchAgents, PreferencePanes and other folders, but that is where such apps as AppZapper and AppCleaner are very nice to have. Also, check the Application website, as often software vendors publish the details of where they install data within OSX, usually in an item called 'manual uninstall'.