1. Creating a observer should be the first to consider.

2. Extending and overriding the core modules should be the second to consider when option 1 cannot fails to accomplish the objectives.

3. Copy the core class to the local directory and put it in the same directory path it was in core directory, this is should be avoided.

4. Modify the core class directly, this should definitely be avoided unless you are just trying to test a code snippet.

First one: When observed a product is added to the cart, print some messages.

Second one: To observe when a product review is submitted. The default Magento behavior is to save the product review with PENDING status, this observer will auto approve the submitted product review instead.

<global> applys to both frontend and backend
<fronend> applys only applys to frontend
<adminhtml> applys only applys to backend

<?php
class MyExtensions_Observerdemo_Model_Observer {
    public function addtocartEvent(Varien_Event_Observer $observer) {
        $event = $observer->getEvent();  //Gets the event      
$product = $event->getProduct();      
$observermsg = "The event triggered>>> <B>" . $event->getName() . "</B><br/> The added product>>> <B> " . $product->getName()."</B>";        //Adds the message to the shopping cart      
echo Mage::getSingleton('checkout/session')->addSuccess($observermsg);  
}  
    public function autoApproveReview(Varien_Event_Observer $observer){      
$event = $observer->getEvent();      
$reviewObjData = $event->getData();      
//print_r($reviewObjData);exit;
        $reviewData=$reviewObjData["data_object"];      
$reviewData->setStatusId(Mage_Review_Model_Review::STATUS_APPROVED);      
        echo Mage::getSingleton('core/session')->addSuccess("Thank you for your input!!");    }}