Resetting a Wii to factory settings
Remember, the answer is based on this official guideline by Nintendo. Basically, you go to the third page of settings of your Wii and then select 'Format Wii System Memory'. Then press 'Format' and TA-DA! Warm note: after you reset it all the data will POOF gone. You can't restore it.
From the Wii start screen select the Wii button in the bottom left of the screen to open up Wii menu:
On the Wii menu select Wii Settings to open up System Settings:
Press the blue arrow 
on the right twice to get to System Settings 3:
Select "Format Wii System Memory".