Open the Find pane and double-click on the Moon’s name. If you get a message saying that the moon is beneath the horizon, click the Reset Time button. Zoom in on the Moon if you want a closer look. Now change the time step in the Control Panel to a discreet value of 1 day. Use the Single Step Forward button in the time mode controls to watch the Moon's phase change day-by-day. You may have to hide the horizon by choosing View->Hide Horizon to keep the Moon in view.