Instructions
From the Wii home screen, drag the Wii Remote to the bottom left corner to the tab that says "Wii." Press "A."
From the menu that appears, select "Wii Settings" by dragging the cursor with the Wii Remote and pressing "A."
Under this new menu for Wii System Settings, select "Wii System Update." When prompted, agree to the update. It automatically will commence unless the Wii is already up to date.