As on a surfboard - you need to pick the right wave at the right time. Swim with your head down looking under your armpit at the wave. As the wave reaches you, you will need to make the next and last stroke a big one - to force your momentum down the wave.
If the wave is smaller, you will stretch out like you would body surf a broken wave, however if the wave is larger, you need to hold your self back from racing down the wave, and instead - spill down the wave with the white water. This can be done like a hydrofoil with your hands out to the side resisting speeding down the wave, the body weight is still forward on the hands - not tilted back. As the wave impacts you can go into your streamline body surfing position, or if the wave is too heavy - you will need to throw the arms back by your side to avoid them getting in the way. When you arrive back at the front of the whitewater - you can bring the hands back out into your streamline position.
There are also ways to body surf like a dolphin - surfing under the water, this is a little advanced but can be done when you became a better body surfer