When paddling efficiently, there are 5 fundamentals you should take in account, for about every stroke you make. There will be exceptions to these 5 cornerstones - as there is for everything - but most of the time you should incorporate them in your stroke:

• torso rotation
• vertical shaft
• catch
• impulse
• paddlers box

 Torso rotation

 Torso rotation has an impact on which muscles you use for your strokes. Basically you can make every stroke with those tiny little arms. Rotating your torso - winding up a spring - and progress the motion from torso rotation puts a lot more power to the stroke. As an extra advantage it's much harder to get totally out of power from your back muscles then it is from you arm muscles.
Torso rotation is present in almost every stroke! Notice the rotated torso for the forward stroke in the following image.

Vertical shaft

Whatever move you want to make in your canoe, your paddle (shaft and blade) should always be at 90° of the direction in which you want to move. This way you use the full power of the blade to move you in that given direction.

Let's have a look at sculling. If the blade is planted vertically in the water, then all of the movement is carried through the blade onto the paddler and the boat, to move the boat sideways. If the shaft hand is wider out then the grip hand, there is a given part of the movement that is resulting in an upward power to the paddler and the boat. That portion of power is lost, since we cannot lift ourselves out of the water. 

So keep it in mind, always have your paddle as vertical as possible on the direction where you want to move to maximize the force in that direction.

catch

The catch is the so called planting of the blade in the water.  Imagine that your blade is a super-freezing device, and the water instant freezes from surface to the bottom of the river/lake. Once firmly planted, you can use the paddle shaft to pull you and your boat forward. You cannot freeze water in the air and let it hang there. So it makes no sense to splash. That's all lost energy.
With a good catch you can use 100% of your energy to move you and  your boat. A bad catch results in some movement of you and your boat, and some displacement of water with your paddle. How much boat movement and how much water displacement you get, is depending on how good your catch is.
The clue is in a good timing, you should give the blade the time to get fully submersed before you start pulling yourself forward. Pulling too soon results in a bad catch, just like pulling too hard will.

In the following image you can see a well planted blade with a good catch. The blade is fully submersed and can be completely moved for an impulse to turn the boat.

Impulse

After you made a great torso rotation, planted a good catch, it's time to pull yourself  forward. The clue here is to do it in an impulsive way, like the martial-arts guys do their strokes. The advantage is that if you're pulling with an impulse, you have a firm grasp on the water, not allowing the water to flow around your blade. If you accelerate too slow, there is always a portion of water that will flow around the blade without having an impact on the forward movement. Then you're just displacing water. So with an impulsive stroke, you are maximizing the resistance of the water against the blade and thus maximizing the power on you and the boat.

Paddlers box

The paddlers box is a virtual box in which the paddle can move around. It is limited by a plane parallel with the shoulders, from the gunwales to the forehead. The width is a a bit wider then the shoulders and the depth is about an extended arm length.

Moving around with your hands and paddle in that box is relative safe for your body. Getting out of that box exposes your body to injuries. No, you won't get injured if you paddle outside the box, but the chances of getting injured in case of an unexpected action or movement are a lot bigger if you're paddling outside the box.

The following image shows a stern pry out of the box:

This paddling position leaves the shaft-arm shoulder in a very vulnerable position. In case a stone, tree or any other object in the water is hit with the blade and the blade is forced upwards, the shoulder is being put under great stress, without possibility to get out of that position.

You should give the box a try, and you'll notice there are some very good reasons why you should stay in the box.