Ejemplo de jQuery Ajax POST con PHP

    A bar
    <input id="bar" name="bar" type="text" value="" />

    <input type="submit" value="Send" />

// Variable to hold request
var request;

// Bind to the submit event of our form
$("#foo").submit(function(event){

    // Prevent default posting of form - put here to work in case of errors
    event.preventDefault();

    // Abort any pending request
    if (request) {
        request.abort();
    }
    // setup some local variables
    var $form = $(this);

    // Let's select and cache all the fields
    var $inputs = $form.find("input, select, button, textarea");

    // Serialize the data in the form
    var serializedData = $form.serialize();

    // Let's disable the inputs for the duration of the Ajax request.
    // Note: we disable elements AFTER the form data has been serialized.
    // Disabled form elements will not be serialized.
    $inputs.prop("disabled", true);

    // Fire off the request to /form.php
    request = $.ajax({
        url: "/form.php",
        type: "post",
        data: serializedData
    });

    // Callback handler that will be called on success
    request.done(function (response, textStatus, jqXHR){
        // Log a message to the console
        console.log("Hooray, it worked!");
    });

    // Callback handler that will be called on failure
    request.fail(function (jqXHR, textStatus, errorThrown){
        // Log the error to the console
        console.error(
            "The following error occurred: "+
            textStatus, errorThrown
        );
    });

    // Callback handler that will be called regardless
    // if the request failed or succeeded
    request.always(function () {
        // Reenable the inputs
        $inputs.prop("disabled", false);
    });

});

// You can access the values posted by jQuery.ajax
// through the global variable $_POST, like this:
$bar = isset($_POST['bar']) ? $_POST['bar'] : null;

$.post('/form.php', serializedData, function(response) {
    // Log the response to the console
    console.log("Response: "+response);
});

    A bar
    <input id="bar" name="bar" type="text" value="" />
    <input type="submit" value="Send" />



<div id="result"></div>

 /* Get from elements values */
 var values = $(this).serialize();

 $.ajax({
        url: "test.php",
        type: "post",
        data: values ,
        success: function (response) {

           // You will get response from your PHP page (what you echo or print)
        },
        error: function(jqXHR, textStatus, errorThrown) {
           console.log(textStatus, errorThrown);
        }
    });

/* Attach a submit handler to the form */
$("#foo").submit(function(event) {
    var ajaxRequest;

    /* Stop form from submitting normally */
    event.preventDefault();

    /* Clear result div*/
    $("#result").html('');

    /* Get from elements values */
    var values = $(this).serialize();

    /* Send the data using post and put the results in a div. */
    /* I am not aborting the previous request, because it's an
       asynchronous request, meaning once it's sent it's out
       there. But in case you want to abort it you can do it
       by abort(). jQuery Ajax methods return an XMLHttpRequest
       object, so you can just use abort(). */
       ajaxRequest= $.ajax({
            url: "test.php",
            type: "post",
            data: values
        });

    /*  Request can be aborted by ajaxRequest.abort() */

    ajaxRequest.done(function (response, textStatus, jqXHR){

         // Show successfully for submit message
         $("#result").html('Submitted successfully');
    });

    /* On failure of request this function will be called  */
    ajaxRequest.fail(function (){

        // Show error
        $("#result").html('There is error while submit');
    });

  $bar = $_POST['bar']

var_dump($_POST);
// Or
print_r($_POST);

// 1. Without JSON
   echo "Hello, this is one"

// 2. By JSON. Then here is where I want to send a value back to the success of the Ajax below
echo json_encode(array('returned_val' => 'yoho'));

 ajaxRequest.done(function (response){
    alert(response);
 });

var ajaxRequest= $.post("test.php", values, function(data) {
  alert(data);
})
  .fail(function() {
    alert("error");
  })
  .always(function() {
    alert("finished");
});

$("#submit_btn").click(function(){
    $('.error_status').html();
        if($("form#frm_message_board").valid())
        {
            $.ajax({
                type: "POST",
                url: "<?php echo site_url('message_board/add');?>",
                data: $('#frm_message_board').serialize(),
                success: function(msg) {
                    var msg = $.parseJSON(msg);
                    if(msg.success=='yes')
                    {
                        return true;
                    }
                    else
                    {
                        alert('Server error');
                        return false;
                    }
                }
            });
        }
        return false;
    });