Hmmm I heard, you would get the e mail in 24 hours.
Personally i got it after around 10 minutes, you only have to reply to the Wii email that is in your inbox. And then your Wii will get a new message from your e mail account. After all these, you'll be able to exchange e mails.
**At least, that's how it's suppose to work. I tried with like 4 different e mails, 2 were my friends' and 2 were my own. I just CAN'T manage to send e mails to the Wii. Its sent, but my Wii never gets it. It's been almost 3 weeks, I'm getting really frustrated with the feature :'(
Haven't tried it with Cellphone emails nor Wii friends yet... Hope those will work fine