Mailchimp is so user-friendly and well thought-out that I want my clients to know about it. It's gained incredible popularity and for so many good reasons. It is free -- up to a certain number of subscribers and emails sent per month -- and is simple to use while it accomplishes some very sophisticated tasks.
Setting up a new mailing list in Mailchimp is easy, and you can import your previous list of subscribers (if you have one.) If you get stuck on a step, it has video tutorials handy that you can view.
It has beautiful templates that you can use or a click and drag interface that allows you to easily format your own template. It allows you to send test emails, and provides tips to help you keep your emails out of the spam folder. It has tools for facilitating posting to Facebook and Twitter. And provides statistics to track the number of opens and clicks that your email generated.
After you set up your mailing list, you'll want to incorporate a subscriber form on your website. Contact me to help with that. I can also help you with your newsletters if you're too busy to handle them on your own.