Edging a Kayak
1. Basic Kayak Forward Stroke
2. Edging a Kayak
Basic Kayak Forward Stroke and Edging a Kayak -
Edging or "taking hull out of the water" on one side of a kayak; induces a turning movement for a kayak.  In other words if you want to turn right, edging your kayak to the left takes hull out of the water on the right, thus inducing a turn.

To do this, lift your right thigh to give the boat some left lean but do not lean your body to the left, instead arch your mid section back to the right.  Thus, your boat leans left and your body leans right...this is called edging a kayak.  It may help to visualize a string from your right pectoral to your right knee and so, even though the kayak is leaning left the distance from your right pec to your knee remains the same.

And...continue paddling forward with a forward stroke.  However, while you edge, you can give emphasis to the left stroke by going wider or staying in longer, thus helping with the right turn.
Edging a Tandem - Or turning without a rudder:
This is the skill of edging but in a wide body, a tandem. So, it is basically a lean and not an edge.

The front paddler's job is to set the ... cadence. The rear paddler's job is to steer the boat.

Turns in a tandem kayak can be executed non-verbally. The rear paddler leans (and paddles wider); when the front paddler senses the lean; she helps lean the boat and also paddles wider...the turn without a rudder is effortless and efficient.
Edging a Kayak by Robert Finlay of Kayak Lake Mead
A kayak hull is symmetrical along the long axis.  It is designed primarily (sea kayaks anyway) to allow the kayak to glide forward in a straight line.  If you take boat out of the water, by edging, then you have unbalanced that symmetry and the boat won't go in a straight line.  So, if you edge the boat to the left, you have taken boat out of the water on the right, the boat's hull sees less resistance and the right and thus turns right. 

Edging a kayak takes a little practice.  Watch the videos below and then get out on the water.   
Kayak Skills - 1. Basic Kayak Forward Stroke and 2. Edging a Kayak
This video shows some turnings and bracings, edging both to and away from the paddle, lever rolls, and re-entries.
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