For the most part, paddling with a double bladed kayak paddle is relatively easy and intuitive. Do what comes naturally and you will get from point A to point B. However, there are a few things to note that, while not critical when it comes to making forward motion, are good to know so as not to look foolish and make more efficient strokes.
When holding the paddle place the wider side of the blade up. You can get more efficient paddling if you adjust your paddle blades so that they are at an angle to one another. Paddles that come apart for travel and storage usually have two or more settings when to snap them together. Choose the one most comfortable for you.
Place your hands as widely apart as comfortable; just a bit more than shoulder width is good. When paddling, place the blade close to the kayak. As long as the blade is fully in the water, deeper is not better.
Alternate your strokes from side to side. You will have a stronger dominate side. Strive to pull with equal pressure to go on a straighter course. Beginners will not realize that much of the power for your stroke actually comes from your torso. Let your body move from side to side as you paddle using the strength of your core muscles to add to the power of your arms.
It is not necessary to grip the paddle tightly at all times. You will tire your hands and for arms needlessly if you do so. To paddle with ease make use of both arms for each stroke. Push with the upper arm and pull with the lower.
For a great video, on this and other basic strokes, check out this lesson on YouTube. http://www.youtube.com/watch?v=_sP2cYu0NX8&feature=related
The best way to turn a kayak is to use the paddle as a rudder. Simply place the blade in the water towards the stern (back) on the side of the direction in which you wish to turn and push away from the Kayak. To make a wider turn without losing momentum place the paddle as far as you can towards the bow (front) of the Kayak on the side opposite the direction you wish to turn. Then make a shallow wide stroke being sure to pull all the way to the stern.
Before trying to kayak on a river with even mild rapids, practice these strokes in calm water. With a little practice in calm water you will be on your way!

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