There is no way to add a page template through the WP-Admin screens in vanilla WordPress.
To create a page template, you simply create a new .php file in your theme’s folder and add this comment to the top:
<?php
/*
Template Name: YourTemplateNameGoesHere
*/
?>
You will then be able to select that template from the page edit screen.
If you’re using a theme developed by someone else, you will want to create a child theme first so that their theme updates don’t erase your edits.
To learn more about creating templates and modding themes, check out these codex entries: