If you don't have any experience canoing or kayaking on rivers, here's something to look out for: moving from still water out into fast moving water, which will tend to tip you over upstream. For example, if you pedal out of an eddy into fast current which is moving from left to right, the current will try to tip you over upstream (i.e. to your left). The Mirage Drive may make this effect more pronounced than it is in a paddle kayak, because the current catches the flippers of the Mirage Drive. You need to anticipate this, and lean fairly agressively downstream (to your right in this example) as you pedal out into current. By this I mean shift your weight onto your downstream buttock, move your shoulder so it's over your downstream gunwale, and pull up somewhat on your upstream carry handle.
If you are paddling a paddle kayak, when you go out into fast current, you can anticipate the effect of the current and stick the power face of your downstream paddle into the water and lean on it. This is called a "high brace," because the paddle shaft is above your hand. Or if you get caught by surprise by the fast current and start getting tipped over upstream, you can stick the back side of your upstream paddle blade onto the surface of the water and lean on it. This is called a "low brace," because the paddle shaft is below your hand. But if you are sitting in a pedal kayak like a couch potato, and don't anticipate the effect of the moving water, here's what will happen: The upstream side of your kayak will get sucked underwater. As the downstream side of your kayak rises up, you'll try to grab it with your armpit. One of your legs and your upstream arm will fly up in the air. And then, bloop, your kayak will be upside down, and you'll be in the water. So anticipate the effect of fast current, and always lean downstream when coming out of an eddy into current.