You can email their Wii once they've added your email address to their Wii address book.
Likewise, on their Wii, when they add your email address to their Wii address book, they will not be able to email you right away - it will send a confirmation email to your email address, and you will have to reply.
To summarize:
To email another Wii from your Wii: add their Wii code to your address book, and have your friend add your Wii code to his Wii address book. Then you will be able to email each other's Wiis.
To email a Wii from an email address: Enter the email address in the Wii's address book. Wait for the confirmation to hit your email address, and then reply to that email. Then you will be able to send email to that Wii from your regular email account, and vice versa.