These waves travel at the speed of light, right? How is light itself affected by gravitational waves? I guess also changed, if they're using lasers to detect them, yea?
The light is affected only because the distance it has to travel changes when spacetime compresses and expands. So the time it takes from A to B changes, but also the wavelength of the light.
What is used in Ligo etc. is interference. They shoot two perpendicular laser beams that collide in a point. Ordinarily, the lasers interfere at this point and everything is aligned so they cancel each other out almost perfectly. But when a gravitational wave changes the length in one of the arms, the interference isn't perfect anymore and you can detect the laser signal.
To a very very good approximation, a gravitational wave front hitting Earth is a flat plane. This means the detectors cannot see waves that hit the arms at close to 45°, as well as waves that hit the Earth's surface close to vertically at the detector location.
So the indication that "gravity wave happened" is wavelength change? Freaky stuff, I really have a hard time wrapping my head around all this, even after reading layman intros.
Mechanical analogy: there are two very long very fine pitch helical gears that are both suspended from one end and mesh perfectly at the other end. When the gravitational wave makes one gear undetectably longer, we can easily see that the gears no longer mesh.
The statement is also only true for perturbations with respect to a fixed background metric. In principle it is possible for space-time to expand much faster than the speed of light (this is believed to have happened just after the big-bang).
Sufficiently "foamy" ones should act like waves passing through material and cause interference based losses while sufficiently strange waves will travel faster than light, a la the hypothetical warp drive using negative mass.