The upward facing dog will not only strengthen your core, it will also increase mobility in your lower back. If your thinking about surfing then you also need to think about strengthening your core. The goal of the pop up is to lift the upper body high enough to get feet and legs under your hips and rear without or barely touching knees on the board. To do this in one fluid motion. You can swim to get in shape and you can do the exercises below, both will help you be a better surfer.
Squats...everyone knows this right? Squat and hold. Back against wall.
Planks... build core strength. Elbows and toes or hands and toes. Tighten tummy. Get more dynamic by bringing one knee up to tummy or chest, return to start and do same with other knee, hold for 15 seconds and repeat. Increase the hold time and reps as you get stronger.
Push ups...do them on your knees to get started if you have to. Make sure your hand placement is inline with your chest and bend your elbows. Go as low as you can and still be able to push up, build your strength and go lower until you're barely touching the floor and push back up.
Pop ups: These are like Burpy's, why called burpy's, who knows?
Step one: squat, lean forward and place hands on floor, kick your legs back and out, put yourself in a push up or plank position.
Step 2: Lower yourself to floor and adjust your hands to be almost parallel across nipples just outside of body. You also may find staggered hands are helpful. One towards chin at or above shoulder and the other aligned with nipples or slightly lower. Which hand goes where? You will decide based on if you like your front foot to be your left or right. I am a "normal" foot ie; My left foot goes in front. So my left hand is slightly higher than my right allowing me to turn my left foot toes right. If you are left foot front then you are goofy foot so switch the hands.
Step 3: In one fluid motion push up with your hands and use your toes quickly bringing your front foot forward, leaving your back foot in same general space. Using momentum, place your front foot forward while turning your knee right or left, this will turn your body and back foot. At this point you should be on your feet facing rt or left depending which foot stays back.
Step 4: Stay low and rise midway hold and visualize that you are now big wave Dave. Repeat. Your feet should be shoulder width and inline with each other, back foot should face the same way you turned and your front foot should be turned as well perhaps not as much. For the most part, your back foot steers your surfboard. Everyone develops their own pop and surfing style. There is no right way or wrong way, if it works for you and its fun, love it and enjoy it.
YOGA.....any Yoga is good but specifically upward facing dog. This is important because surfing is all about weight shifting this position puts weight back so you dont "pearl". Its the beginning of the "pop"