Actually, to be friendly with you, there is no such thing as a comment box
in HTML or web development. There are just a bunch of HTML elements, that you avail in your website to create a function that would work for the users, to post the comments. For example, take an example of the following form in your website, which you design as to be as much simple as it can be and the user would understand that he is supposed to write the comment in it.
<p>Post your comment below:</p>
<input type="text" name="comment" />
Adding a submit button is another topic, whether to send the comment through press enter function or not and other bla bla.
Then there comes the next thing, to post the comment. Web development and the W3.org don't have any such methodology or standard for comments. Once again it is you, trying to avail the server-side coding technique to create a function to store the data that he sent to your server in such a way that once when you will take it back out, it will be as if they were comments.
You use different technique, like database storage mediums to store the data of the user in the database to query it back.
Tip: I would recommend that if this is a public blog, or any such relative website then you would/should use the already present comment service, such as Disqus