First of all you need a router . The only way to connect to the Internet for Wii is by using Wi-Fi . If you connect to the internet you will be able to access the Wii-Shop Channel , your Mii's will be able to roam in your friends Wii's if you activate their MINGIE , you will be able to access the Weather and News channel too and so on ...
Here we go :
1.Go to Wii Options in the lower left.
2. Click on Wii Settings to the right.
3. Pres + to go on page 2.
4. Now on page 2, click on Internet.
5. Then click Connection Settings.
6. From this list, click Connection 1.
7. Then, click Wireless Connection...
8. Now click Search for an Access Point.
It will start looking for access points . Click you're Access Point when it finishes listing all of them and connect to it . It will test your connect and if it's good it will tell you : Click OK to update Wii .
9. Now, back in Wii System Settings, click on WiiConnect24.
10. From the following list click WiiConnect24.
Click On and then Confirm to save your settings. This feature allows for updates to be seemlessly sent to your Wii so you don't have to do the final step every time.
Ok, the final steps, just as a way to make sure your Wii is up to date. Click the right arrow from the 2nd page of Wii System Settings.
11. Click Wii System Update...
12. click yes...
It will test your connection for a few seconds... Then an update screen may quickly come up and tell you there is an update (whether or not your Wii actually needs one)
Now you can go back to Wii Menu . That's it
Enjoy