Good posture is key if you are to use your body efficiently. Sit straight, relax your shoulders, and open your chest for ease and efficiency of breathing. Don't lean against the backrest.
Keep your legs together with feet against the footpegs. Adjust the footpegs so that your knees are bent slightly and you are able spread and press them against the kayak for extra balance if needed. Keeping your legs together allows better torso rotation and makes paddling more efficient.
Be sure that you have proper footpegs you can push against.
Your torso and legs will do most most of the work. Your shoulders and arms are only there to transmit power. To learn the principle, try paddling by rotating your torso and keep your arms absolutely straight.
When you place the blade in the water, imagine your are pulling yourself up to and past the paddle.
At the start of your stroke, coil your torso so that you place the blade in the water up by your feet and close to the kayak's waterline. Keep your lower arm almost straight. Relax your upper arm with a slight bend so that your upper wrist comes a bit closer to your eyes.
Press your stroke-side foot firmly against the footpeg. Sink the blade into the water with a spearing motion.
Begin the paddling stroke by uncoiling your torso and keeping the lower arm near straight. Keep pressing the stroke-side foot against the footpeg to support the stroke. Try to generate more power at the beginning of the stroke, less at the end. That way you create power with the strong muscles of your torso, and right when your paddle is in the water at its most favourable angle.
Keep your upper arm relaxed and hold the paddle loosely, so your muscles can rest. Keep your upper hand at about eye level, and allow your upper hand to move across your body, to keep the paddle vertical.
End the stroke when your lower hand is about level with your your belly. Continuing further would feel natural, but it just slows you down.
After the stroke, move the blade out of the water to back and away from the kayak. Lift the blade out of the water by leading with the elbow. and allowing the wrist to follow. Take care not to lift your elbow above shoulder level. Let your upper arm follow the rotation of your torso.
After you lift the blade from the water, prepare for the next stroke. Keep coiling your upper torso so that you can start the next stroke as far forward as possible.
Try to maintain a continuos flow, but focus on each paddling stroke. Remember that paddling forward is not the same as paddling in a straight line, so keep reading the following tutorials also.