Before geting the details of a customer you must to have check whether Customer is Logged in or not, If a customer is logged in then only you can get details fo the customer. Then write the code below to get customer details

 
$customer = Mage::getSingleton('customer/session')->getCustomer();
$email = $customer->getEmail();// To get Email Id of a customer
$firstname = $customer->getFirstname();// To get Firstname of a customer
$lastnam e= $customer->getLastname();// To get Last name of a customer