Modern users typically download "Forwarder" WADs. These small files create a shortcut on your Wii Menu that launches a specific homebrew app (like WiiMC-SS) from your SD card. How to Install WAD Files on Your Wii
The original official YouTube WAD can still be found online, but it is now non-functional because the servers it connects to have been shut down. youtube wii wad download
Critical note: The console’s hardware (88 MB of RAM, 729 MHz processor) is too weak to handle modern YouTube’s HTML5 player or ads. Modern users typically download "Forwarder" WADs