To play Newer, you'll need a few things:

Wii console
NSMBWii disc
SD card
SD card reader
Wii or Wii U Console
The Wii Mini is not yet supported.
New Super Mario Bros. Wii game disc (or a ROM dump if you'll be playing with Dolphin Emulator).
SD or SDHC card (if you'll be playing on a Wii) or SD card (if you'll be playing on a Wii U) with at least 570 MB of free space, formatted to FAT.
A way to access SD/SDHC cards from your computer.