A good surf fitness program is going to include some variety. There should be a couple different things you can choose from to work on individual aspects of surfing.
Surf Fitness Program - Arms
To work your arms and keep them up to surfing you can do a couple different things. You can do push-ups, or pull-ups. Either of these will also work your back or chest which you will be using to do all that paddling on the surf board. If you would rather do something with weights you could try chest presses or butterflies. These don't have to be heavy weights. In fact, doing additional sets with lighter weights would be ideal for surfing.
Torso
A surf fitness program that targets the torso should include exercises that will strengthen the torso. You may not realize it, but pulling yourself up on the board into your stance is going to require the strength of your middle. The stronger you make these muscles the better chance you have of being able to pop up faster. Sit-ups are classic for strengthening those stomach muscles. Doing inverted sit-ups will target the lower stomach muscles more than traditional sit-ups.
Legs
You should do a couple different things when considering your legs. You will need strength, but you will also need balance. Balance may seem like it would be hard to practice, but you could add in a stability ball or just practice standing on one foot. Make sure to do this with both legs, and work on being able to stand for longer times. For strength you could work with weights doing leg presses or leg curls. Again, remember that it doesn't have to be a tremendous weight. Lighter weights with more reps would be better for a surf fitness program. If you want to work the legs without weights, try doing lunges or squats.
Surf Fitness Program - Aerobics
Aerobics should be part of your surf fitness program. Surfing is a sport that requires a lot of energy, and conditioning your body to do the work would be a good idea. Aerobics are really rather simple. You can do things like jogging, jumping rope, or even jumping jacks. As long as you do these at a steady pace for a little bit, keeping your heart rate up a little, it's aerobics.