Enter the 16-digit code into the Wii U Nintendo eShop, and the download for the DLC will begin. Once finished, the DLC will be available on Super Smash Bros. for Wii U.
Please close the Super Smash Bros. for Wii U software after purchasing DLC. The installation of the content will complete on the Wii U menu. You may then restart the software, and the DLC will be available.