Custom additional post view

I’m coming to WP from Drupal. I’ve got a good PHP background and I’ve used WP casually for a while but never really looked under the covers. Now I’m interested in giving it a go.

I want to add an additional view to each of my existing posts based on an optional URL parameter. So I want to keep example.com/path_to_my_post/ rendering on single.php, then add example.com/path_to_my_post/special/ and have it render with another template file (say my_special_tpl.php).

I assume this will be a custom plugin. Can someone point me towards the relevant area of the docs and/or plugins that use the API in similar ways?
I’ve got no problem with the functionality in my_special_tpl.php I’m just not sure how to get it routed correctly.

Thanks!