The paddler's box is a position to hold your body in while paddling. To get in the box, first figure out how to hold your paddle. Hold the paddle above your head with its midpoint directly above your head. Move your hands outward toward the blades until your elbows are at approximately a 90-degree angle.
While keeping your hands in the same position and elbows slightly bent, lower the paddle in front of you. This is the paddler's box. It's called a box, because your body is in a box-like shape.
To see this shape, imagine hovering above your body and looking down. Your arms form two sides of the box; the paddle's shaft and the imaginary line running between your shoulders form the other two. Maintaining the position forces your body to torso rotate and helps protect your shoulders from injury.
Maintain your paddler's box with your arms out in front of you and twist your upper body side to side. Make sure you are twisting from your hips and waist. This movement is called torso rotation. Torso rotation allows you to use your strong core muscle groups instead of just your arms to power your kayak. Strong torso rotation is key to efficient and enjoyable paddling.
The forward stroke is the stroke you use to move your kayak forward. Get in the paddler's box and torso rotate your right paddle blade forward. You're going to catch the blade into the water at your right foot. Once the blade is fully submerged, unwind your torso using rotation until the blade is at or just past your hip and then release the blade from the water. Repeat for your left blade. For more power, as you unwind your torso apply foot pressure on submerged blade's side.
The back stroke, also known as the reverse stroke, is used to stop the kayak and paddle in reverse. When you have a powerful enough back stroke, you should be able to stop the kayak within three strokes on each side. For the back stroke, torso rotate backwards and put the blade in the water behind you, then unwind the blade forward. Maintain your paddler's box throughout the stroke.
A draw is used to move the kayak sideways toward your paddle's blade. It's a useful stroke for docking, coming abreast of another kayak and in rescues. It can also be used to help avoid obstacles. For a basic draw, torso rotate completely to one side so your shoulders are parallel to the center line of the kayak. Reach out and plant the blade as far away from the kayak as possible. Then pull your kayak toward the blade using torso rotation.
A sweep is an exaggerated forward stroke in which you try to keep the paddle as far away from the kayak as possible. It's used to turn the kayak. Your kayak will turn away from whichever side you're sweeping on. To sweep, assume the paddler's box and torso rotate your blade far forward. As you unwind, sweep the blade out away from the kayak in a wide arch until the blade reaches the rear of the boat.
A reverse sweep is used to turn the kayak toward the side of the boat you're sweeping on. It's performed just like the sweep stroke, but starting in the stern of the boat and ending forward. By combining a reverse sweep on one side and a sweep on the other, you can pivot your kayak 360 degrees in place.
It's best to learn these strokes from a qualified instructor by taking an intro to kayaking course. Contact the American Canoe Association to find an instructor in your area.
To practice torso rotation, put a big beach ball between you and your paddle. Forward paddle while keeping the beach ball on the deck of your kayak. You should twist in the kayak.
Practice the reverse sweep and forward sweep combo until you can pivot your kayak 360 degrees in eight strokes or less. This will help you develop a good sweep stroke for fast turns.