You need some server-side code to process that form. The easiest way to do this is to sign up with a service like CampaignMonitor or MailChimp. They give you the code you need to paste into your page, and the rest is handled by their system. I use CampaignMonitor. Users can sign up to your newsletters, and it's really easy to send out emails, and users can do forwards, unsbscribes etc. very easily, and you get great stats on how many emails were opened, who opened them etc.