You will find two important components when it comes to surfing balance. The 1st of these will be strong and stable leg muscles. Training your legs in isolation can iron out any weaknesses possibly you have in your lower leg and hip muscles and decrease the possibility of injury.
The 2nd component is key stability. This refers to keeping the body stable when other forces making the effort to knock you lower.
Single-leg stability and strength: Barefoot, Single-Leg Dead lifts, unweighted or with a light dumbbell in the opposite hand. Barefoot, Side Lunges holding a dumbbell in front, up by the chin. Promotes trunk activation.
Core stability - keeping the trunk stable while parts around it are moving. Think about your core as the clutch to a manual car. Planks, athlete's planks and variations, tacos (laying flat, raising the arms and legs to meet at the center. Can also be done with a Swiss ball), bicycles, leg raises, side planks.
Flexibility - especially in the hips. See my other post in surfing workouts for more insight. Cheers!