Here’s how I added Disqus to Ghost’s Casper theme. In the post template (post.hbs), look for

{{!--
<section class="post-full-comments">
    If you want to embed comments, this is a good place to do it!
</section>
--}}

and change it to

<section class="post-full-comments">
<div id="disqus_thread"></div>
<script>
  var disqus_config = function () {
    this.page.url = '{{url absolute="true"}}';  // Replace PAGE_URL with your page's canonical URL variable
    this.page.identifier = 'ghost-{{comment_id}}'; // Replace PAGE_IDENTIFIER with your page's unique identifier variable
  };

  (function() { // DON'T EDIT BELOW THIS LINE
    var d = document, s = d.createElement('script');
    s.src = 'https://your-short-code.disqus.com/embed.js';
    s.setAttribute('data-timestamp', +new Date());
    (d.head || d.body).appendChild(s);
  })();
</script>
</section>

making sure to replace your-short-code with your actual short code.

Then find the line

{{/contentFor}}

and add the disqus count script line above it, like:

<script id="dsq-count-scr" src="//your-short-code.disqus.com/count.js" async></script>
{{/contentFor}}

again, replacing your-short-code with your actual short code.