You are making sense, but you seem to misunderstand the concept of sending emails.
HTML is parsed on the client side, while the e-mail needs to be sent from the server. You cannot do it in pure HTML. I would suggest writing a PHP script that will deal with the email sending for you.
Basically, instead of the MAILTO, your form's action will need to point to that PHP script. In the script, retrieve the values passed by the form (in PHP, they are available through the $_POST superglobal) and use the email sending function (mail()).
Of course, this can be done in other server-side languages as well. I'm giving a PHP solution because PHP is the language I work with.
A simple example code:
form.html:
<form method="post" action="email.php">
<input type="text" name="subject" /><br />
<textarea name="message"></textarea>
</form>
email.php:
<?php
mail('[email protected]', $_POST['subject'], $_POST['message']);
?>
<p>Your email has been sent.</p>
Of course, the script should contain some safety measures, such as checking whether the $_POST valies are at all available, as well as additional email headers (sender's email, for instance), perhaps a way to deal with character encoding - but that's too complex for a quick example ;).