I needed a way for a user to login to a Magento shop from an external website. Let's see step by step how to do this.

Download code Demo
Step 1:

First off you'll need to create an API user. You can follow this tutorials to create an API user.

Make sure this user has access to at least "Customers->Retrieve customer info".

Step 2:

You'll obviously need a form on your external site for the customer to enter their login details. 

The following is just an example form to give you a rough idea.

Please note: You'll notice I've included an iframe pointing to the shops login page, this is important as it will create the required cookies for the customer to login. If you don't include this iframe any customer who is missing the required cookies won't be logged in.

Step 3:
We need create login page into external site, from where user can enter their login details to login to Magento site. Let's create a php file (externalLogin.php) for external site. Add following code to externalLogin.php file.

<iframe src="http://www.demo.com/customer/account/login/" style="position:absolute;height:1px;width:1px;top:-100px;left:-100px;"></iframe>
<form action="http://www.demo.com/externallogincheck.php" method="post">
    <div class="login_field">
        <label for="login_username">Username</label>
        <input id="login_username" type="text" value="" name="login[username]" />
    </div>
    <div class="login_field">
        <label for="login_password">Password</label>
        <input id="login_password" type="password" value="" name="login[password]" />
    </div>
    <div class="login_field">
        <input type="submit" value="Buy selected product" />
    </div>
</form>

Note: Change www.demo.com with your magento site url. Put this file in root of your external site.

Step 4:
Now we need to add a php file to magento root to check the details user posted from external site with above code is valid or not. Add a php file (externallogincheck.php) to root of your magento site and add following code.

function validatePassword($password, $hash) {
    $hashArr = explode(':', $hash);
    switch(count($hashArr)) {
        case 1:
            return md5($password) === $hash;
        case 2:
            return md5($hashArr[1].$password) === $hashArr[0];
    }
    return false;
}
$apiUrl = 'http://www.demo.com/api/?wsdl';
$apiUser = 'YOUR API USER';
$apiKey = 'API PASSWORD';
 
if(isset($_POST['login'])) {
    try {
        $client = new SoapClient($apiUrl);
        $session = $client->login($apiUser, $apiKey);
    } catch (Exception $e) {
        echo $e;
        exit;
    }
    
    
    //Lookup customer record
    list($customer) = $client->call(
        $session,
        'customer.list',
        array(
            array(
                'email' => addslashes($_POST['login']['username'])
            )
        )
    );
    if(is_array($customer)) {
        if(validatePassword($_POST['login']['password'], $customer['password_hash'])) {
            
            require_once 'app/Mage.php';
            umask(0);
            Mage::app()->setCurrentStore('default');

            Mage::getSingleton("core/session", array("name" => "frontend"));
            $session = Mage::getSingleton("customer/session");

            //Log out any existing sessions
            if(!$session->isLoggedIn()) {
                $session->logout();
            }
   
            //Log user in
            $login = Mage::getSingleton('core/app')->getRequest()->getPost('login');
            $session->login($login['username'], $login['password']);

            header('Location: http://www.demo.com/');
            exit;
            
            exit;
        } else {
            header('Location: http://www.externalsite.com/externalLogin.php?ref=invalid');
            exit;
        }
    } 
    else {
            header('Location: http://www.externalsite.com/externalLogin.php?ref=invalid');
            exit;
    }
}

Note: Change www.demo.com with your magento site url and www.externalsite.com with your external site url. Put this file in root of your magento site.

Download code Demo