How to bind an action after customer login success using Magento?

On the Mage_Customer_Model_Session model's method setCustomerAsLoggedIn() an event customer_login is being dispatched. I guess you need to hook in on that event. You could do this as follows.

Add the event to your module's config.xml file (app/code/local/Lpf/ModuleCookie/etc/config.xml):

<?xml version="1.0"?>
<config>
    <modules>
        <Lpf_ModuleCookie>
            <version>0.1</version>
        </Lpf_ModuleCookie>
    </modules>
    <global>
        <models>
            <lpf_modulecookie>
                <class>Lpf_ModuleCookie_Model</class>
            </lpf_modulecookie>
        </models>
    </global>
    <frontend>
        <events>
            <customer_login>
                <observers>
                    <lpf_modulecookie_customer_login>
                        <type>model</type>
                        <class>lpf_modulecookie/observer</class>
                        <method>customerLogin</method>
                    </lpf_modulecookie_customer_login>
                </observers>
            </customer_login>
        </events>
    </frontend>
</config>

Now create a model Lpf_ModuleCookie_Model_Observer (app/code/local/Lpf/ModuleCookie/Model/Observer.php). Add a customerLogin() method to the class:

class Lpf_ModuleCookie_Model_Observer
{

     /**
      * Run couple of 'php' codes after customer logs in
      *
      * @param Varien_Event_Observer $observer
      */
     public function customerLogin($observer)
     {
         Mage::log(__METHOD__ . '() Hello!'); // Remove afterwards. Check your var/log/system.log to see if came to this point
         $customer = $observer->getCustomer();
         // "run couple of 'php' codes"
     }

}