1. First off, you need to make sure you have NO custom stages saved on your Wii or SD card. Not even the three sample stages. You can either move them to your SD card and then to your computer, or just delete them altogether.
2. Open up the hackmii_installer folder you downloaded earlier and copy the boot.elf file into the root of your SD card. Don't worry about any of the other files for now.
3. Finally, copy the "private" folder from the Smash Stack download onto the root of the SD. If you already have a "private" folder there, rename that folder to "privateold" or something.
The root of your SD card should now have these files:
Now, insert your SD card into your wii and boot up Smash Bros. Go to the stage builder screen and the game will crash and start loading the Hackmii installer.
Now you will see a screen similar to this.
Select continue. Don't worry if it says that BootMii can only be installed as an IOS, just hit continue. (Side note: you will not be able to use the Wiimote right now, but you can use either a Gamecube controller or the buttons on the Wii. Power=move cursor, Reset=Select)
Select the 4th button, which takes you to a new option. Select the first option there, what it does is back up the Wii's NAND memory (it'll take a long time and you need at least 512 MB of space on the SD card.)
Congratulations, you have successfully installed the Homebrew Channel on your Wii! Next post, we'll take a look at the Homebrew Browser and start applying patches to games.