The first point to make about the reverse stroke is that you hold and orient the paddle exactly as you do for the forward stroke. You'll apply the back of the blade - the non-power face - to the water.
Theoretically, the reverse stroke should be just like the forward stroke, only backwards. You want to plant the paddle near the stern, guide it toward the bow, and recover at the hip. The trouble is that our bodies are not reversible so we can't use the same motion both ways. Let's begin with torso rotation. Without a rear-view mirror, you need to rotate effectively just to see where you're going (very important). Start with a maximum rotation to one side. As you look behind you, plant the paddle well astern, close to the hull. Be sure the blade is perpendicular to the kayak and the paddle shaft is in line with the boat (your offside hand should be over the water above the onside blade). Because of the awkwardness of this position, people often set the angle of the blade at a slant relative to the kayak. This causes unwanted boat turning and occasional colorful language. As you begin the stroke, push down on the paddle to gain a little support. Complete the stroke by rotating toward the midline, maintaining the path of the blade parallel to the hull. Do this by keeping your offside hand over the onside edge. Slice the blade out of the water when the shaft is vertical. The stroke should be short. If the blade goes too far, it will turn the boat. On the recovery, rotate maximally to the opposite side and repeat the process. Support the action with alternating foot pressure, just as in the forward stroke. To make minor course corrections, sweep the paddle out away from the boat instead of next to it.
Don't hurry! It's much trickier to maintain and correct your course in reverse than it is paddling forward. Stay focused, and don't forget to look where you're going.