To use WAD files, your Wii must be "softmodded" with the Homebrew Channel. You will also need a tool called a (like Yawmm or Pimp My Wii ).

A (rare and often impractical) conversion of the game to be installed internally. Forwarder WADs vs. Full Game WADs

Since SSBB is a massive dual-layer disc game (nearly 8GB), it is too large to fit on the Wii’s limited internal system memory. A "Forwarder" acts as a shortcut. When you click the Brawl channel icon, it automatically tells an app like USB Loader GX to launch the game from your external storage.

Once finished, press the Home button to return to the Wii Menu. You should see a new Super Smash Bros. Brawl channel! A Note on Safety and Bricking

Place your .wad file into a folder named wad on the root of your SD card.

These are almost non-existent for Brawl because the Wii only has 512MB of internal storage. You cannot install an 8GB game as a standard WAD. Why Use a WAD for Super Smash Bros. Brawl?

Locate the Brawl Forwarder WAD and select "Install."