If you don't know about Club Nintendo, check it out here:
You can basically register select Nintendo hardware and software for Club Nintendo Points that you can then redeem for cool stuff at the Club Nintendo Store! This is some pretty exclusive stuff by the way!
I'm not sure if the Virtual Console stuff applies across the board, or only from select Nintendo titles here as well. The Virtual Console of course consists of: WiiWare Games from 3rd party publishers and Virtual Console games that are re-released versions of your old favorites from: Nintendo 64, Super Nintendo, NES, Genesis, Dreamcast, and more.
Anyway, all that background aside, here is what you want to do:
1. Create your Club Nintendo account, if you don't already have one
2. Power up the Wii and click the Wii Shop Channel
3. Click "Settings"
4. Select "Link Your Club Nintendo Membership"
5. Enter your Club Nintendo Username and Password in the form
6. Click "Link"
And you are finished! Simple enough right? And the best part...now any time you download WiiWare or Virtual Console games they will be eligible to earn Coins to use in your Club Nintendo account!