If you look to your left, you may notice me paddling a black and white cedar-strip and canvas canoe. I am not about to dump into the water---the "lean" is proper solo canoeing posture. A few years decades back, I was the canoeing director at a Canadian summer camp and taught hundreds of kids how to paddle a canoe. Since this is a "science blog", I'll explain this awkward-seeming posture to you.
The proper position for traditional Canandian-style solo paddling is half-way between the bow and the stern, leaning to the side you paddle on, preferably on your knees. The lean itself accomplishes two things: it brings you closer to the water, making paddling easier, and it lifts a substantial portion of the hull out of the water. Less hull in the water means less resistance to forward motion and to turns. You kneel, rather than sit on the (decorative) seat so that you have a low center of gravity and wide base of support---canoes are rather tippy vessels.
Once seated thus, paddle in hand, you can achieve complete control of the canoe. The position described puts you at the fulcrum of the canoe, and your paddle is a powerful lever. To pull your paddle straight into the canoe is called a "draw" (the opposite of a draw stroke is often called a push-away). If you draw right at the fulcrum, you will move (approximately) sideways. If you reach behind you and draw, you will pivot the stern of the canoe toward your side, turning the canoe to the "outside" (away from your paddling side). Reach forward and draw, and your canoe pivots the other way. You may wish to refer to my well-rendered schematic.
Understanding the pivot allows you to move forward in a straight line without switching sides. A standard forward paddle stroke (known as a "bow stroke") turns you to the outside and makes you look rather silly if your objective is forward motion. A deceptively simple twist of the paddle at the end of a bow stroke turns it into a J-stroke. The end of the J-stroke is a "push-away", so the first part of the stroke turns you to the outside, the last part pivots you back to the inside. When executed well, the result is smooth, forward motion.
While achieving perfect control of the canoe may take a while to master, the basic concepts are reasonably simple and easy to build upon. For example, when paddling into a strong wind, it often helps to move yourself forward in the canoe, allowing the bow to "cut" through the waves (also increasing the drag so that the wind doesn't push you around---a sort of "flag in the wind" phenomenon). With the fulcrum moved forward, however, you must reach much further backward with your J-stroke in order to go straight.
With just a wee bit of science, you can figure out how to make a canoe do what you want it to. How cool is that?