What you want to do is relatively simple, as long as you know how to create a table in a DB, insert and retrieve data from it.
Another option is to use some sort of file-based system, whereby you write the user comments to a file and read that file when assembling the output for the page.
The idea is as follows:
1) Save the posted values from the form to a file or database.
2) When the page is loaded, write a script that reads the file or pulls records from the database.
3) Display those records on the page under the article.
I suggest you search GOOGLE for a simple guestbook or shout-box tutorial that you can read and modify for what your specific needs are.
Here is one such article: http://www.spoono.com/php/tutorials/tutorial.php?id=19
ANd here is another: http://webmaster.lycos.co.uk/topics/technic/php/php-workshop7/0/
Hope that helps.