There are too many ways to identify is user logged in or not in magento.

<?php 
    if(Mage::getSingleton('customer/session')->isLoggedIn()){
$customerData=Mage::getSingleton('customer/session')->getCustomer();
echo "<pre>" print_r($customerData->getData());    //    
    }else{
 //not logged in
    }
?>

We can check user logged in or not in outside magento.

require_once 'app/Mage.php'; // Magento Mage.php path
umask(0);
Mage::app('default');
Mage::getSingleton('core/session', array('name' => 'frontend'));

$user = Mage::getSingleton("customer/session");

if($user->isLoggedIn()) {
  echo "Logged";
} else {
   echo "Not Logged";
}

// Through helper to <strong>check the user login or not in magento</strong> file.
<?php if ($this->helper('customer')->isLoggedIn()): ?>