A good way to think of paddling is to compare it to ballroom dancing - the man's side if he is doing it right. When dancing, we maintain a nice erect posture. We use our arms pretty much like struts to signal to our partner where we want to go. We don't crush her hand, we have a nice relaxed grip.  We try to keep an eye on where we are going so we don't run into other obstacles (dancers for instance). Although we are sitting in a kayak, the basics are pretty much the same. This approach makes good use of our core muscle groups instead of pulling with just our arms. Here is a great article on paddling posture and the Paddler's Box: Paddling Posture.

In river kayaking, we often have to put in at non-optimal locations along river banks.  There may be a drop-off, slippery surfaces, moving water, or other challenges.  A good practice is ensuring you have at least three solid points of contact when entering/exiting your craft.  This is often two feet on land and a hand holding the craft or two hands stabilizing the craft and placing one foot at a time inside the boat.  The paddle float rescue in deep water depends on this principle - tripods can be very stable.  Here's an article on this subject from the ACA: Boarding a kayak from shoreline.  Keeping your weight low is also far less tippy.  That is also demonstrated quite clearly in the paddle float rescue.  

In the previous article, we talked about using the whole body. In this lesson, we will concentrate on the core muscle groups.  Beginning paddlers use their biceps more than any other muscle group. They tire very quickly, especially on long flat water paddles. Racers and experienced boaters use the arms more like struts and pull the paddle blade through the water with their abdomin, pectoral, shoulders, and upper back muscles. Compare the size of those muscle groups against the much smaller biceps and you can easily understand why seasoned boaters can paddle all day and make it look effortless. Here is a good article on an efficient forward stroke from a racer's perspective:  Racer's Efficient Forward Stroke.

Many new to the sport think paddling is all about the arms.  Although you can paddle pretty much with the arms, you will tire very quickly if you do so.  Seasoned paddlers use their torso as much as possible to take the load off their arms.  They also push off the foot bulk head with the same side foot with each paddling stroke.  Most of the body works together to get the maximum power out of each stroke.  Here is a good video demonstrating torso rotation: Torso Rotation Demonstration.