A comment box is an HTML element that can allow user to add some values, it can be a single line input field or a multiple line textarea element (or a
contenteditable="true"
div element). User can add the comment, that is not a problem.
The actual thing is the background code that would actually save that _comment of user_. You're using PHP, you can use MySQL as the back-end data source. Just extract the value from textarea (or what ever element you're using to allow the user to enter values) and then store that data in the database.
There is nothing fancy about a comment-box, the actual thing is how you store them and when you store them (either by a post-back like submitting or by pressing enter key). You should also give
this old answer[
^] of mine a read.