To run the game in windowed mode, you do need to first set the game's resolution to a value that is less than your desktop resolution, so that the window will be smaller than your desktop. Otherwise the window would be bigger than - or equal to - the desktop and so the game just stays full screen.
For example, if you run your computer desktop at 1280x1024, go into Wizard101's Options and set the game to 1024x768 or to 800x600. Then try changing to windowed mode. Remember, change the game's resolution, not your computer desktop's.
Like most Windows applications, you can also press Alt-Enter to toggle windowed mode on and off - but, again, only if the game resolution is lower than the desktop.