Updating wii system menu
To find out what version of the operating system you have, go into Wii Options, click on Wii Settings and check the number on the upper right corner of that screen. Now you reinstall the Homebrew Channel for the appropriate OS.
When you get the Homebrew Channel back, make sure to turn off update checks and don't opt to upgrade your Wii again to prevent this from recurring.
At the moment, 4.1 is the most recommended firmware. 4.2 did not add any positive capabilities to the system, only tactics for hindering homebrew (all of which have been bypassed at this point using methods described on the Hack Your Wii page). All firmware is fully hackable, with varying degrees of issues.
Firmware 4.1 is the same as 4.0 with only one difference. There is no need to remain on any firmware below 4.0.
Turn on the Wii by pressing the power button on the remote or the console. Click the "Wii" menu in the bottom left-hand corner of the screen.
Move the cursor over to "Wii Settings," and select it by pressing "A." Click on the right-facing blue arrow, and click the "Internet" command on the second settings page.
You will be presented with the Wii System Settings 1 page.
Select "Connection 1" from the list of connections, and then click "Wired Connection" to begin the connection test.
Make sure that the wireless router is broadcasting (there is usually an indicator on the router that shows this).
Firmware 4.1 includes a fix for a bug with Wii Sports Resort. If you are on a firmware below 4.0, then you are missing out on SDHC support and the ability to store games and channels and launch them from the SD(HC) card.
For more detailed information on the differences between firmware/System Menu versions, review the System Menu page on Wii Brew.