An online e-mail account is convenient because you can set it up and access it from any computer -- and delete messages you don't want your child to see from any computer, too. While there are many online e-mail providers to choose from, Gmail is my choice because it's easy to set up, has a nice uncluttered inbox, offers a large amount of storage for old messages, and gives your child access to other cool tools like a customizable search page, document creator, and calendar. Go to mail.google.com and click on "Sign up for Gmail."
[NOTE: Since Google, like most websites, frequently changes its design and presentation, some of the details and screenshots in the steps that follow may not look exactly like what you're seeing. However, they should give you a good enough idea that you can find your way through the sign-up and setting process.]