If you want to run a newsletter/mailing list, there are a few different approaches and options how to go about this. Which one you want to pick mostly depends on your requirements, technical expertise and preferences. The spectrum reaches from very simple, web interface based management systems over more sophisticated and more customizable sytems to independent client applications that run on your local computer and provide the mailing list management and actual bulk-mailing. For starters, you might want to look at Bravenet's mailing list service:
Usually you want a facility on your website to enable people to subscribe to or unsubscribe from the list. I'm afraid you wouldn't be able to integrate the HTML code for the subscribe/unsubscribe options etc. into your Website Maker based site, as it doesn't support the integration of HTML code. So, you would have to work around this and find another way for people to contact you regarding subscriptions and cancelations (e.g. a contact form or e-mail address) and manage the mailing list manually. That's probably ok as long as your list doesn't grow too big.