Go to the Letterbomb page. Before downloading, you need to select your OS version (viewable in the Wii's settings menu). You also need to input your Wii's Mac Address. To find this, click on Wii Options, go to Wii Settings. Go to page 2 of the settings, then click on "Internet". Click on "Console Information". Enter the Mac Address displayed there in the appropriate area of the website page.
By default, the option to "Bundle the HackMii Installer for me!" is checked. Leave it that way.
The page has a "recaptcha" security system. After filling in the words, you have a choice between clicking "Cut the red wire" or "Cut the blue wire." I clicked the "red wire" button, but as far as I can tell it doesn't make any difference which one you click. Either will download the file.
Unzip the file to your SD card.
Note: If you have a brand new Wii, this reportedly won't work until there is at least one message in your message board. If your Wii is new and you have no messages, create a memo on your Wii before going on to the next step. To create a memo, go to the Wii Message Board by clicking the envelope in the little circle on the lower right corner of the main menu, then click on the create message icon, then the memo icon, then write and post a memo.