Ajax In Magento using module

Write your code to hit the module in script tag
<script>
function api(id){
jQuery.ajax({
type: "POST",
url: "<?php echo $this->getUrl('ankur') ?>",
data: { id : id }
})
.done(function( msg ) {
//alert( "Data Saved: " + msg );
});
}

</script>

Now create a module 
location: /public_html/app/code/local

module name(create folders):Excellence\Test\controllers/IndexController.php
<?php
class Excellence_Test_IndexController extends Mage_Core_Controller_Front_Action{
public function indexAction(){

// Write here ajax action, what you want to do...

}
}

?>

now create another folder Excellence\Test\etc\config.xml

<?xml version="1.0"?>
<config>
    <modules>
        <Excellence_Test>
            <version>0.1.0</version>    <!-- Version of module -->
        </Excellence_Test>
    </modules>
    <frontend>
        <routers>
            <test>
                <use>standard</use>
                <args>
                    <module>Excellence_Test</module>
                    <frontName>ankur</frontName>  <!-- This is the URL
 of the module. i.e www.yourmagento.com/index.php/test will be the url of your module. -->
                </args>
            </test>
        </routers>
    </frontend>
    <global>
        <blocks>
            <test>
                <class>Excellence_Test_Block</class>  <!-- Path of the
 Block Folder, where all php files are located related to view -->
            </test>
        </blocks>
        <helpers>
            <test>
                <class>Excellence_Test_Helper</class> 
<!-- Path of Helper Files -->
            </test>
        </helpers>
    </global>
</config>

now create another folder Excellence\Test\Model\Observer.php

<?php
class SmashingMagazine_LogProductUpdate_Model_Observer
{
    public function logUpdate(Varien_Event_Observer $observer)
    {
        echo "ankur";
    }
}

At last in etc/module
create a .XML file with Modulename_Subfoldername

<?xml version="1.0"?>
<config>
    <modules>
        <Offer_Test>   <!-- Name of Module -->
            <active>true</active>  <!-- This says if the module is active or not -->
            <codePool>local</codePool> <!-- This says the location of the module i.e inside the local folder. It can also be community folder. -->
        </Offer_Test>
    </modules>
</config>


Thats all................ hope this will work.