How do I create a page template that doesn’t show URL, sidebar, nav menu, footer?

You can achieve that functionality by loading your template in a hidden div with z-index greater than that of a overlay div. now when clicked on any image you can use jquery to show the hidden div and the overlay. The overall process can be summarized as below:

1. Create a overlay div anywhere in your page(say home page).Suggested to be below your footer as below:

   <?php get_footer();?>
   <div id="overlay"></div>
   

2. The css for the overlay would be like this:

   #overlay {
   position: fixed;
   top: 0;
   left: 0;
   width: 100%;
   height: 100%;
   background-color: #000;
   filter:alpha(opacity=50);
   -moz-opacity:0.5;
   -khtml-opacity: 0.5;
   opacity: 0.5;
   display:none;
   z-index: 1000;
    }
   

3. Now create a hidden div that will load your template as below in your page:

   <div class="myclass" style="z-index:1001;display:none;"><?php load_template('path_to_your_template_you_want_to_load.php');  ?></div> 
   <a class="click_img"><img src="https://wordpress.stackexchange.com/questions/126590/url to image you want to show" /></a>
   

4. Now include a script that will show your hidden div when clicked on the image as below:

   jQuery(document).ready(function(e) {
   jQuery('.click_img').click(function(e){
   e.preventDefault();
   var winY = jQuery(document).scrollTop();
   var y = 1.04*winY;
   var winX = jQuery(window).width();
   jQuery('#overlay').show();
   jQuery('.myclass').show();
   jQuery('.close_button').show();
   });
   
   });
   
   jQuery('.close_button,#overlay').click(function(e){
       jQuery('.myclass').hide();
       jQuery('#overlay').hide();
       jQuery('.close_button').hide();
       });   
   }); 
   

5. Now note that the close button in your template to be loaded must have the class close_button.

   <div class="close_button"></div>
   

6. Now it’s up to you to design your close button.