Step one: Ensure your vWii is hacked and has The Homebrew Channel (or HBC for short) installed. This typically requires the Wii U as a whole to be hacked and have CFW installed, which if anything is even better.
Step two: Obtain a WAD of the Photo Channel, then place it on your SD card. You'll also want something like WiiModLite to install it.
Step three: Open HBC from the Wii Menu, launch a WAD manager (like WiiModLite) and install the Photo Channel wad. Congrats!