In a one-plane swing, you're moving your arms around your torso. In a two-plane swing, your arms need to stay in front of your body. The way to visualize this is to imagine turning your shoulders while making a karate-chop move with your left arm.
Practice hitting draws and fades with just your left hand, picturing the toe of your club closing and hitting the outside edge of the ball for a draw and remaining open and hitting the inside edge for a fade. The weight of the club will encourage the up-and-down movement you need.