Homebrew Hax.

Ohai. Diz is Paul. I will teach you how to do Homebrew on yer Wii.
First, yoo need a Wii. This should be self explanatory. :)
Then check what your System Menu version is. You can do this by going to
the "Wii" button then pressing the "Settings" button. You can see the version
at the top right of your screen.
If it says anything between 3.0~4.1, click here.
Bannerbomb for Wii System Menu 3.0~4.1
If it says 4.2, you must click on this link.
Bannerbomb for Wii System Menu 4.2
Unzip your respective file. I hope you know how to do that.
Hackmii Installer
Unzip that too. :)
Now for the moment of truth : readying your SD card.
On your SD card, copy and paste the bannerbomb folder (go into it until "private", then copy and paste that folder chain).
Grab the boot.dol from the Hackmii Installer folder, and place that in the root of your SD card.
Place the SD card in your Wii.
If you are on System Menu 3.0~4.1, go from Wii Button->Data Management->SD Card. Press OK on the popup.
If you are on System Menu 4.2, simply press on the SD card button on the System Menu. That easy. Then press OK on the popup.
I think you should know how to navigate the installer. INstall the Homebrew Channel and DVDx for sure.
Bootmii, however, is your decision. If you CAN install it (meaning you have an older Wii), it can save you in a lot of tight situations.
However, it is a bootloader patch. Thus, it has the smallest chance it can break your console. So it's your choice.
Exit the installer with your installed Homebrew, and enjoy. For an introduction on how to use apps on the Homebrew Channel
go to the "Animal Crossing" tab. During the beginning of that tutorial, you will install the Homebrew Browser.
Enjoy!