Since this isn't a licenced game for the Nintendo Wii, first you'll need the Homebrew Channel installed. This requires that you use The Legend of Zelda: Twilight Princess disc to install it (it's only required once, so if you don't own it, go rent or borrow it for a day, you literally only need it for 5 minutes). You can also install it if you have a modchip and haven't updated your Wii yet. For instructions to install the Homebrew Channel, see the installation instructions.

Once the Homebrew Channel is installed (or you already had it installed), the installation of Supersonic Wii itself is simple. Just extract your downloaded archive into the root of your SD (or SDHC) card, so that the "apps" and "data" folders are merged to the card. You don't need this README file there, of course, so you can ignore/delete it.

And that's it! Just extract this download to an SD card and you're ready to play. Start up the Homebrew Channel and pick Supersonic Wii from the menu.