Running Newer Super Mario Bros. Wii in Dolphin Emulator.
Download a Development or Beta version of Dolphin Emulator that is at least version 5.0-15520 (released November 2021). This may be obtained HERE*.
Run Dolphin once before continuing to ensure the folders you will be editing are generated.
* - On Windows, you need the Visual C++ Redistributable to run the latest versions of Dolphin.
** - On Linux, check your package manager for updated Dolphin builds. Otherwise, you will have to compile Dolphin yourself. Instructions HERE.
Download the Newer Super Mario Bros. Wii package from HERE and locate "NewerSMBW" and "riivolution" folders, then put them into the default Riivolution Dolphin mod folder.*
* - On Windows, "%appdata%\Dolphin Emulator\Load\Riivolution" (to get here, press the Windows Key+R, and enter that directory with or without the quotes).
[Note: if you've ever opened a version of Dolphin earlier than 5.0-18242, it will instead be "%userprofile%\Documents\Dolphin Emulator\Load\Riivolution"]
** - On macOS, "~/Library/Application Support/Dolphin/Load/Riivolution" (to get here, open Finder, press ⌘+Shift+G, and enter that directory without the quotes).
*** - On Linux, it may be either "~/.dolphin-emu/Load/Riivolution" or "~/.local/share/dolphin-emu/Load/Riivolution"
Now, open Dolphin. Ensure that New Super Mario Bros. Wii is in your list of games. If you can't see it, open "Config" and navigate to the "Paths" tab. Then, add the folder containing your New Super Mario Bros. Wii ROM.
Now, right-click New Super Mario Bros. Wii, and click on "Start With Riivolution Patches..."
A window will pop up allowing you to configure your Riivolution patches. Make sure the option is set to "Enabled" and click "Start" to launch the game.
Make sure other hacks aren't enabled as well!
Newer is up and ready to be played. Have fun!