DISCLAIMER:
For this guide, you are gonna need to install the Homebrew and Riivolution channels on your Virtual Wii of your Wii U console. You also need a disc copy of NSMBW, an SD card and a PC.
STEP 1: Extract the contents of the .zip
STEP 2: Insert your SD card to your PC
STEP 3: Move all the extracted contents to the root of your SD card.
STEP 4: Insert your SD card to your Wii
STEP 5: Launch the Virtual Wii then Riivolution (From the Homebrew Channel or from the Main Menu)
STEP 5½: Click install if you don't have the Riivolution Channel installed yet for easy access from the main menu
STEP 6: Disable all the other mods you have and enable ChillySMBW, then click Launch
STEP 7: Enjoy!