An oar has the flat part, the part that goes in the water, on one end and a handle on the other. They go in oarlocks, mounted to the side of the boat. The movement you make with the oar will always pivot around the oar lock.
A paddle can also have a handle at one end, often in the shape of T, such as the type used for a canoe. You can move the paddle anywhere you want.
A kayak paddle has a blade on either end, and you hold it in the middle. You put one side in the water to propel the boat forward, then the other. By the way, tell him to make sure he's using his body, not his arm, and don't think of pulling the paddle toward him, but of keeping the paddle in place and pushing the boat past that point.
You can use the verb "to paddling" or "go kayayking" to refer to the activity, by the way, though "go padding" has meaning only to those who do it.