The only thing one needs to do is to add codes to blog htmls.

Disqus

Before adding any code you need to register at Disqus. Then configure your Disqus short name as a token specified. Now you’re prepared for adding a Disqus comment block.

<div id="disqus_thread"></div>
<script>
    /**
     *  RECOMMENDED CONFIGURATION VARIABLES: EDIT AND UNCOMMENT THE SECTION BELOW TO INSERT DYNAMIC VALUES FROM YOUR PLATFORM OR CMS.
     *  LEARN WHY DEFINING THESE VARIABLES IS IMPORTANT: https://disqus.com/admin/universalcode/#configuration-variables
     */
    /*
    var disqus_config = function () {
        this.page.url = PAGE_URL;  // Replace PAGE_URL with your page's canonical URL variable
        this.page.identifier = PAGE_IDENTIFIER; // 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-name].disqus.com/embed.js';

        s.setAttribute('data-timestamp', +new Date());
        (d.head || d.body).appendChild(s);
    })();
</script>
<noscript>Please enable JavaScript to view the <a href="https://disqus.com/?ref_noscript" rel="nofollow">comments powered by Disqus.</a></noscript>

MathJax

That’s easy to add Disqus, right? It’s even easier to configure MathJax for you even needn’t sign up for any website. Assume you’ve coding experience in LaTeX. If not, visit here for tutorial.

<!-- LaTeX support -->
<script type="text/javascript"
  src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>

<script type="text/x-mathjax-config">
MathJax.Hub.Config({
  tex2jax: {
    inlineMath: [['$','$'], ['\\(','\\)']],
    displayMath: [['$$','$$'], ['\[','\]']],
    processEscapes: true,
    processEnvironments: true,
    skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'],
    TeX: { equationNumbers: { autoNumber: "AMS" },
         extensions: ["AMSmath.js", "AMSsymbols.js"] }
  }
});
</script>
<!-- LaTeX Support -->

Attention that according to MathJax (April 18, 2017),

The MathJax CDN hosted at cdn.mathjax.org will be shutting down on April 30, 2017. Current and future releases available on other CDN providers.

So you should select a third-party CDN for processing your LaTeX codes. For more information, visit here.


Update:

New MathJax snippet with CDN provided by Cloudflare:

<script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-MML-AM_CHTML'></script>