How to make a non-Drupal page and where to place it?
You need to create a custom module and implement hook_menu() for you custom page.
Here you get details about hook_menu "https://api.drupal.org/api/drupal/modules!system!system.api.php/function/hook_menu/7".

To get this link on user menu tab use type as
 'type' => MENU_DEFAULT_LOCAL_TASK
And write your page code by calling a function
'page callback' => 'user_details',

create user_details function and write code for custom page.