The part of the Form tag you are interested in is the "action" parameter. This tells the browser what page/script will process the form when you click on the Submit button.
You can try adding action="mailto:me@email.com" to the form tag, but, not all browsers support this. If it does, you will get an attachment by email with the form data in one long string. It's not pretty, but, it's easy.
The only way to make this work for all browsers is to use a web script (PHP, Cold Fusion, Javascript, CGI) to collect the form data and send it by email.