Facebook comments box is a social plugin provided by facebook. In order to implement that, you need to perform the following steps:-
Go to the following URL:-
https://developers.facebook.com/docs/plugins/comments
Fill the form, and click on the button named "Get Code".
Clicking on this button will give you a code. Copy that code and paste it in your page. This is also usually a step which can be broken in two steps:-
1) Paste the javascript SDK on your page in the body tag. This code is given below:-
<div id="fb-root"></div>
<script>(function(d, s, id) {
var js, fjs = d.getElementsByTagName(s)[0];
if (d.getElementById(id)) return;
js = d.createElement(s); js.id = id;
js.src = "//connect.facebook.net/en_GB/sdk.js#xfbml=1&version=v2.3&appId=751348078240642";
fjs.parentNode.insertBefore(js, fjs);
}(document, 'script', 'facebook-jssdk'));</script>
Step 2).
Add the following Code where you want comment box to appear:-
<div class="fb-comments" data-href="http://developers.facebook.com/docs/plugins/comments/" data-numposts="5" data-colorscheme="light"></div>
Please Note following:-
There is an data-href attribute in the code which is pasted in step 2. You need to replace the value of data-href with the URL of the page where you have added comment box.
I am giving an example of Step 2 on MVC View where I have used the Comment box.
<div class="fb-comments" data-href="@Request.Url.ToString()" data-numposts="5" data-colorscheme="light"></div>
You can see that I have replaced the value of the data-href attribute at run time with the actual URL of the page.