The call goes to:
http://yourdomain.de/index.php/newsletter/subscriber/new/
But form data is sent via post as you can see in the Mage_Newsletter_SubscriberController newAction, where you find the following line of code.
$this->getRequest()->isPost() && $this->getRequest()->getPost('email')
So you need to name your form field 'email'
Good luck!
Edit:
Just use something like this:
<form action="http://yourdomain.com/index.php/newsletter/subscriber/new/" method="POST" id="newsletter-validate-detail">
<input type="text" class="input-text required-entry validate-email" name="email" id="newsletter">
<input type="image" src="path to image" name="submit" />
</form>