REVISION The code is located outside of magentos scope

<?php
//MAGENTO CONNECTION AND CUSTOMER INFORMATION
require_once '../../app/Mage.php'; // location of mage
umask(0);
Mage::app('');
Mage::getSingleton('core/session', array('name' => 'frontend'));
$session = Mage::getSingleton('customer/session');           
//Zend_Debug::dump($session->isLoggedIn());
if(!Mage::getSingleton('customer/session')->isLoggedIn())
    Mage::getSingleton('customer/session')->setBeforeAuthUrl(Mage::helper("core/url")->getCurrentUrl());
?>

LOGIN SECTION (PHP)

switch($_REQUEST['action']) {
    case 'login':
        try {
            $login = $session->login($_POST['username'],$_POST['password']);
        } 
        
        catch(Exception $e) 
        {
            echo $message = $e->getMessage();
            echo 'Click <a href="WERE YOU WANT TO LINK">HERE</a> To login';  
        }
        header("Location: ");  //REDIRECTS IF SUCCESSFULL
        break;
 
    case "logout":
        $session->logout();
        header("Location: "); // REDIRECTS WHEN YOU LOGOUT 
        # Redirect or give a status message, etc
        break;
 
    default:
        # If the customer is not logged in, show a login form
        # If the customer is logged in, show a logout button
        if($session->isLoggedIn()){ ?> LOGGED IN CODE <?php } else { ?> NOT LOGGED IN <?php } ?>

LOGIN FORM

<form method="POST" action="index.php">
            <label for="username" >Email</label><br />
                <input type="text" name="username" size="40" /><br /><br />
            <label for="password" >Password</label><br />
                <input type="password" name="password" size="40" />
            <input type="submit" name="submit" class="button-link" value="LOGIN" />
            <input type="hidden" name="action"  value="login" />
        </form>

This is basically a self submitting form, mage app will check the user supplied info run the action and create a session. Let me know how you get on :)