Reverse cross deck and reverse J are, for me, the two major reversing strokes.
For most canoeists one of the strokes will be favoured above the other, for me the cross deck, but it is important to try both to see which you prefer and learn the element of each stroke to expand your paddling potential.
How to Reverse J
The reverse J is very similar to the forward J stroke but in reverse. Start by rotating round and extending the paddle out almost flat against the water. Then, push forward until the paddle is along wide the waist and begin to rotate the paddle, unlike the forward J the, so that your top thumb points to the sky. Now you have a bow rudder to correct the direction of the canoe. Repeat this stroke and with practice you should maintain a straight line. But remember to look where your going, turning round every 2 or 3 strokes to check where your going. It is also advisable to pick something to look at I front of you on the line you want to go, to help maintain a straight line.
How to reverse cross deck
The correction in this stroke comes from a stroke on the off-side. So begin with a simple stroke on the on-side, rotating round and extending to get the best possible stroke. Then when the paddle passes the waist remove the paddle. And here comes the difficult part. The aim is to rotate your body round to face away from your usual paddling side and place the paddle in the water with the opposite side of the paddle that you just used facing the direction you will paddle. Most people will cross their arms and not get the full potential of the stroke. What you are aiming to do is rotate your chest round to get the paddle to face as if you where taking a forward stroke in the direction you should now be facing. This stroke is good as well because it forces you to face backwards on every stroke to see where your going.