I often fly fish from a canoe. On busy water, I float from spot to spot and then wade fish. I easier water, I am comfortable fishing while the canoe drifts. Trick number one is to pay attention to weight distribution. The heavy end of the boat will naturally tend to go downstream first. If you are by yourself, sit backwards on the front seat and pack your heaviest gear in front of the center thwart. Weighted that way, the canoe might still tend to spin as you drift down stream. When I am by myself on the river and fishing while I float, I don't try to fight the spin. I just let the canoe do it's thing and move back and forth between sitting backwards on the front seat or facing forward while sitting on the center thwart. It's all great fun except when you have to try to land a fish and paddle at the same time.

Get a copy of Bill Mason's "Path of the Paddle". It is an excellent primer on using all of the traditional paddle strokes and on reading running water.