Essentially I'm attempting to show something similar to "Viewing PageNumber of TotalNumberOfPages" in every subpage for any specific parent page. And so i am trying to puzzle out how you can count the amount of sub-pages/child pages which exist and display them on the subpage?

You should use count(get_pages('child_of' => page_id)) to obtain the quantity of sub-pages. But to be able to display it's for instance page 2/5 you need to define somewhere which sub-page is which number. I'd suggest you accomplish that inside a custom area. Just put 1, 2, 3, 4, 5, correspondingly inside a custom area in every page that you simply call number or something like that.

To develop Calle's answer.

//get the sub pages for the parent page
    $subPages = get_pages('child_of'=>parent_page_id);
    //$i will equal the page number
    foreach($subPages as $subs){
        //not sure what the exact array key for page_id will be. use var_dump($subPages)to find out
        //make the array key the page id for use later (as current_page_id)
        $pageNumber[$subs->page_id] = $i;
    $numberPages = count($pageNumbers);

Then show the page count and number pages for that page you are well on.

echo 'vewing page '.$pageNumber[current_page_id].' of '.$numberPages;