Another item you should consider is a Lycra top. If there's a lifeguard, ask if there's a current running north or south. Anytime there's a nor'easter, the current can carry you several blocks south in just minutes. A south swell can do the same in the opposite direction. Don't be embarrassed to ask a surfer coming out of the water what it's like.
Most surfers are usually glad to help.
Practice standing up or riding on your stomach until you're comfortable. When your fins scrape the sand, it's time to get off. Probably the most important thing to master is standing up quickly and smoothly. It determines if you'll make the wave and where you'll end up. As if doing a push-up, move in, quick motion, kicking your legs into a squatting position, then rising slowly.