The Twilight Hack is currently the only safe, public way to enable homebrew on an unmodded Wii. The Twilight Hack is achieved by playing a hacked game save for The Legend of Zelda: Twilight Princess which executes a homebrew application from an external SD card.

The latest release is compatible with version 3.3 of the Wii System Menu.

http://www.wiibrew.org/wiki/Twilight_Hack