You need to login to your WordPress admin area to create a new page or edit an existing one.
On the page editing screen, scroll down to the ‘Page Attributes’ section, and you will find a template drop down menu. Clicking on it will allow you to select the template you just created.
Template list will show only if you are viewing a screen for editing a Page: page templates are not a default option for posts or custom post types.
It is not every WordPress theme that has multiple page templates, if a theme doesn’t have multiple page templates the option will not be visible, since there is no page template you can switch to. You can always create a new page template though.