Kayaking - holding the paddle
As you probably know, one of the differences between kayaking and canoeing is the paddle that's used. When kayaking, the paddle that's used has a blade on each end of the pole. When paddling, you will be using [simultaneously] a push and a pull on the paddle. This is one of the elements of kayaking that creates a very energy efficient way to propel yourself thru the water. If you've ever rented one of those boxy row boats at a lake you've experienced the exhaustion when going between 2 places. Kayaking allows you to split the energy and to spread your exersion between 2 motions. This helps to prevent fatigue.
Your primary source of power is NOT your arms, your torso is your primary power source. Using too much arm power is a sure way for you to tire yourself out.
When gripping the paddle, your control hand (typically the right hand) stays in the same place. This hand will hold the shaft with your knuckles lined up with the upper edge of the paddle. The hand opposite your control hand (usually your left) will have a relatively relaxed grip on the shaft. This allows you to rotate the paddle as necessary for your grip. Your arms should be out in front of you with an elbow bend of slightly more than 90 degrees.