How do you paddle a canoe? That depends! At first though, you'll only need a few strokes to get started. Later you can perfect some fancier strokes that will let you move the canoe any which way you please, or let you move at a good clip silently so you can float alongside some loons without bugging them! We'll just deal with the basics here, though.
The forward stroke is what the person in the front should be doing. All of their strength should be going into making the boat go forward. Make sure you're paddling in a straight line and don't follow the curve of the boat! It's hard, but the paddler in the front must resist the urge to steer! That's entirely the responsibility of the person in the stern (back) of the canoe, you'll end up working against them if you try. Just paddle consistently and straight back. They'll get a feel for how much your paddling turns the canoe and eventually get in the groove of making up for it.
If you want to go forward without turning, you want the J-stroke! You'll be using this stroke more than any other if you are paddling in the stern (back) or solo, so get good at it! The trick is in how you "feather off" - turn the paddle as you push off at the end. When you paddle straight back, the canoe will turn a bit towards the side you're paddling on. Feathering off is done to cancel out that turning so that you ultimately go straight.
The sweep is used for moderate to large course corrections. The paddler in the bow or the stern can do the sweep and it'll have the same effect. When I use the sweep, it's because my canoe's heading is far off course and I want to correct it quickly. If you're doing this often, you're doing something wrong!