In the U.S. (Hawaii) you won’t need to be GDPR compliant. There are anti-spam laws that have to be followed, like being able to opt out, have a physical address and lots more. Most people who are managing a mail list, use an outside service such as Mailchimp or one of its many competitors. Most offer free accounts for smaller lists and ensure that you are compliant to any legal requirements.
You would need to add the signup form on your site, and there are stacks like post-office mentioned above that can make that easier. Or you can usually get an HTML snippet from the provider.
As for composing the newsletter providers like MailChimp have online templates to build mailings like newsletters online. If you need something a bit more complicated than you can have a look at this post: