Wordpress - How do I get the current edit page ID in the admin?

You can also use

$post_id = $_GET['post'];

Or you can use a hook (probably better).

function id_WPSE_114111() {
    global $post;
    $id = $post->ID;
    // do something
}

add_action( 'admin_notices', 'id_WPSE_114111' );

You will need to add a conditional since this will run on all admin pages, I recommend using get_current_screen();

For example to run only on pages:

function id_WPSE_114111() {

    global $my_admin_page;
    $screen = get_current_screen();

    if ( is_admin() && ($screen->id == 'page') ) {
        global $post;
        $id = $post->ID;
        var_dump($id);
    }
}

add_action( 'admin_notices', 'id_WPSE_114111' );

You can add this code in functions.php file and it will give you a meta box above the publish settings box when editing a post or page.

 <?php

function cf_post_id() {
    global $post;

   // Get the data
   $id = $post->ID;

   // Echo out the field
   echo '<input type="text" name="_id" value="' . $id . '" class="widefat" disabled />';
  }

 function ve_custom_meta_boxes() {
    add_meta_box('projects_refid', 'Post ID', 'cf_post_id', 'post', 'side', 'high');
    add_meta_box('projects_refid', 'Page ID', 'cf_post_id', 'page', 'side', 'high');
   }
   add_action('add_meta_boxes', 've_custom_meta_boxes');

?>