I attempting to hook a function into save_post such as this:

function my_function($post_ID) {
add_action('save_post', 'my_function');

However , it isn't doing anything, I am while using var_dump as example however it should a minimum of print the $post_ID variable after i edit/create a publish.

Shall We Be Held missing something? Thanks ahead of time!

Where are you currently by using this? So far as I understand, the "save_publish" hook is just performed within the admin section, which means you will not see anything if you're attempting to run this outdoors from it.