For strength training, all you need is 6 types of exercises with 2 sets and 15 repetitions for each set. Cable trainers are great but free weights can also work. Do exercises that will target your abs, chest, legs, arms, and back. With stronger body frame, the more you will be able to handle difficult waves.
Plyometrics will be able to provide you explosive bursts of energy which is what you need if you are a surfer. Exercises will include leapfrogging across the floor, jumping squats, and indoor rock climbing. You can try practicing surfing pop-ups over and over again as this is a good plyometrics exercise.
Cardio is a very important type of training for surfers. Always remember that surfing is all about stamina and cardio exercises can give you more stamina. You have to remember that surfing will involve long stretches of paddling as well as long distance swimming. Using a treadmill is a great way to develop your stamina. And, another fantastic cardio training is swimming. You can also use an elliptical trainer.
Also, you need to remember that flexibility is important in surfing. It will also help avoid injuries. For this, you can take yoga classes. Or, you can simply do stretching exercises before and after you workout. It is also recommended that you should do stretching exercises before you hit the water to surf. This will make you more flexible and also prepare your body for a brutal beating which is exercise.