Let's review what you discovered about riding the waves. First, facing the shore, position your kayak 90 degrees to the direction of the waves. Then, to catch one …
Paddle strongly as it lifts the back of the boat.
Leaning forward helps the boat accelerate to stay on the wave.
Use a stern rudder for some directional control and support
If you do it perfectly, you'll have a nice schuss forward. Less than perfect, and the wave will slue you sideways. Instead of surfing, you'll be broaching. This is where the moves you practiced in Exercise #6 will save you from a capsize.
Why you broach: When you're on a wave, the water under the back of your boat is moving faster than the water under the bow of your boat. Unless the push from behind is dead straight, the boat will slue to one side or the other. To see the effect, put a pencil on your desk and try to push it in a straight line with one finger on the eraser.
What to do and when to do it: Imagine a clock face, with your bow as "12". As long as your bow is between 11 o'clock and 1 o'clock you'll stay on the wave. But the moment that your bow veers past 11 or 1, your stern rudder won't keep you straight on the wave. You're broaching and you have maybe two seconds to do the following:
Get off your stern rudder
Let the boat turn side-to the wave
Edge into the wave and go to a low brace
This is the exact move you used when waves were shoving you sideways in Exercise #6. Our intrepid paddler is doing it perfectly.
As the wave passes, straighten up and use sweep strokes to turn back on course.
In case of a capsize. Another reason that learning to always edge into the wave is important is because the safest way to capsize is to fall into the wave, not away from it. Rolling into the wave is safer for two reasons. First, your wet exit will practically be automatic: the wave will probably pull you out of your boat as it passes. Second, you'll wind up with the boat between you and the beach. As long as you are seaward of your boat, the next wave can't pick it up and bash you with it. So no matter how you go over, get yourself to the seaward side of your boat. Then catch hold of a toggle and let the boat stream away from you while the waves push you towards the shore or help arrives. Keep your arm bent, so that it can act as a shock absorber for your shoulder when the waves hurl the boat shoreward.
A final word to the wise: Naturally, you are too smart to venture into surf big enough to capsize you without 3-Star skills and an expert guide. This article is intended as an introduction only.