Hmmmm, likely not any time soon. Remember that the force of gravity is 1E36 times weaker than the EM force. A gravitational wave is essentially space itself stretching and compressing. So like on the ocean unless the wave is crashing against the shore, you will just bob up and down as the wave passes by, surfing no where. Where do gravitational waves crash against a shore? I don't know. So you should probably try surfing on EM radiation first, as this will be way easier. Though it is easier to sail ( on EM radiation that surf on it. Also, you can surf electrons on a plasma wave.
There is no net "force" I can see on a point particle being illuminated by a GW. I would also think that the only means of momentum transfer is by scattering of gravitational waves from your board. Good luck with that one.
Given that the lower the energy of the wave and the longer and faster it moves, the longer your board needs to be (we Santa Cruzan's know these things)... I'd say you need an extremely long one and extremely light weight. Be prepared to spend$$$$4444
Max, Gravitational waves do not produce a displacment of the center of mass of an object. A gravitational wave propagating in the Z direction will convert a sphere into an oscillating ellipsoid which alternately stretches and shrinks the X and Y directions without a net volume change. Also, the gravitational wave propagates at the speed of light, so you are never going to move this fast.
More seriously, I think, in contrast with some of the comments made before, that in principle a gravity wave would indeed propel an appropriate kind of surfboard. Think for instance of a gravity wave like the one recently detected in LIGO but instead of looking at it from the Earth, looking at it from nearby the colliding black holes (say at a few million kilometres) . The gravity wave would have a huge amplitude, and thus a large enough surf board ( in fact any object) floating in empty space will deform due to the passing of the wave. This in turn will lead to the objet to develop an oscillating quadruple moment in its mass distribution and thus to emit gravity waves in many directions. Those secondary gravity waves will interfere with the original gravity wave, leading to some nontrivial patterns f constructive and destructive interference that will result in 3- momentum being carried away from the board in an anisotropic fashion. This will result in a net impulse transferred to the surf board. Symmetry considerations clearly indicate that such impuse will be along the direction of propagation of the original gravity wave.
So yes ... get a large enough, massive and readily reformable object to play the role of your surfboard... get copse enough to a couple of colliding black holes and you will be ready.
Since we have all drawn to the conclusion that a body in the line of path of a gravitational wave will experience a displacement away from the source of the gravitational wave. This should be the source of Dark energy.