The keys to side surfing success are a combination of edging your kayak and bracing. You need to lean and brace into the wave to keep it from knocking you over. 
The most important element to your success in staying upright is the edging of your kayak. If you do not edge your kayak with the deck leaned toward the wave, you will capsize when hit. Sitting straight up in the kayak with no edging is a guaranteed capsize. Edging the kayak in the wrong direction (deck leaning away from the wave) not only means a capsize, it means a very fast capsize.

After edging your kayak, you need a brace to keep yourself upright after impact, and to help get your upper body back over the balance point of your kayak while it is still edged and side surfing toward shore. In photo A, the kayaker is ready for the wave to impact the side of the kayak. The kayak is edged correctly. Keep in mind that the larger the wave, the greater the edging that's needed. Notice how her upper body is balanced over the boat. Upon impact of the wave (photo B), the kayak is knocked out from under the kayaker. She is ready to fall toward the water on the wave side with a brace ready to keep her from going under. The brace gives her the opportunity to balance her upper body over her kayak again. The sooner she can re-balance over her kayak photo C the more control she will have while side-surfing toward shore. In big waves, edging alone isn't enough. You may have to throw your body into powerful waves with your paddle in a brace position so you won't capsize. After the impact of these large waves, you can regain your balance over your kayak, but still maintain the edging as you move quickly toward shore.