Why your canoe keeps turning
If you always paddle on the same side, you push the stern sideways and the bow swings the other way. That's not clumsiness, just simple physics: one sided power turns any boat.
As long as you do nothing about it, you slowly curve away from your paddling side. The fix is either to switch sides regularly or to correct your course while you paddle.
The J-stroke keeps you on course
The J-stroke is the trick that lets you stay on the same side and still go straight. You pull through as usual, and at the end of the stroke you turn the blade and push it gently outward.
That little move at the finish nudges the stern back and cancels out the turn. The path of the paddle looks like a J, which gives it its name. At first you might overdo the correction, but after a few strokes you'll get a feel for it.
Two people in the canoe
With two of you it actually gets easier once you coordinate. Paddle on opposite sides so your turning forces cancel each other out. Keep the same rhythm, it runs smoother and you wobble less.
The person in the back has the overview and steers, correcting the course with the J-stroke. When an arm gets tired, just call out and switch sides together, that way you stay on a straight line the whole time.