How to get input value from html form in jQuery?

This will do what you need:

$(document).ready(function(){
    /* Watch OnSubmit for all forms */
    $('form').submit(function(e){
        e.preventDefault();

        /* Show the 'commentonpost' for the submitted form */
        alert($(this).children('#comentonpost').val());
    });
});

This works, but you should keep in mind that your document is not valid because you have elements that have the same IDs. IDs must be unique within a document for it to be valid.

You may only need to change this part:

$(document).ready(function(){
  /* The following code is executed once the DOM is loaded */

  /* This flag will prevent multiple comment submits: */
  var working = false;

  /* Listening for the submit event on all the forms: */
  $('form[id^=addCommentForm]').on('submit', (function(e) {
    var submitted_form = $(this);
    //etc...

when you use jquery to select an ID, it will return 0 or one elements that match, and it will match the first one it finds. from http://api.jquery.com/id-selector/

Calling jQuery() (or $()) with an id selector as its argument will return a jQuery object containing a collection of either zero or one DOM element.

whenever you use $("#submit") its parsing through the DOM and finding the first instance of <input type="submit" id="submit" value="Submit" /> and returning that element. what you really want to do in your to scope your search down. you know you want the input from the form that was submitted, so you should try

$(this).find("#submit")

this will start at the form element, and search only elements contained inside the form for the first element with an ID of submit.

update

didnt realize your event was only tied to the first form, this whole things needs some work.

you've got a generic form template, and when you've got multiple forms like this, you really shouldnt be giving them all the same ID. instead, start binding event handlers to classes, and use the dom to store whether a form is 'working' or not as well

http://jsfiddle.net/neKdz/3/

I would suggest something like this

$(document).ready(function(){
    $(".add-comment-form").submit(function(e){
        var x = $(this).find("#comentonpost").eq(0).val();
        // now you have number x of submitted form and you can do the rest
    }); 
});

Edit:

To prevent page reloading because of form submission, add onSubmit="return false;" on form elements, e.g.:

<form class="add-comment-form" id="addCommentForm3" method="post" action="" onSubmit="return false;" >

But because of this we have to follow another approach using click event:

$(document).ready(function(){
    $("#submit").click(function(e){
        var x = $(this).parent(".add-comment-form").eq(0).find("#comentonpost").eq(0).val();
        // now you have number x of submitted form and you can do the rest
    }); 
});

Combination of click event and cancelling submit event should work. But just for the record (you should already know this, but I can imagine you might have a reason for doing it) using same id on multiple html elements is not a good strategy.