The best and easiest way is just to use the Wii web browser to log into a web-based e-mail account like Gmail, Hotmail, Yahoo, etc.
You can also add e-mail addresses to your Wii address book (which can be accessed via the message board), but each one has to be added, then the owner of the e-mail account has to accept the invite before you can exchange messages. It's not really worth the bother.
