You will want to learn in a progression, starting with an introductory kayaking class where you will learn the basics. Once you are comfortable handling a kayak in calm conditions, you can consider taking a beginner's surf kayaking course. After gaining confidence and control in the surf zone, you are ready for higher level clinics where you can learn more complex maneuvers as well as surf forecasting, risk assessment, and rescue skills.
Organizations such as the American Canoe Association (ACA) and the British Canoe Union (BCU) offer surf kayaking training programs for paddle surfers and their coaches. While your instructors may be closely affiliated with a local paddle shop, club, or school, they are likely to have obtained training and certification through one of these national organizations.