So what are these things and how can we detect them?
First, a quick review. Mass causes a warp in space and time. The sun's "gravity" isn't a pulling force, it's really an indentation that the sun causes in the space around itself.
Planets think they're moving in a straight line, but they're actually pulled into a circle while traveling through this warped spacetime. Go home planets, you're drunk.
The idea is when mass moves or changes, Einstein said that there should be gravitational ripples produced in spacetime.
Our problem is that the size and effect of gravitational waves is incredibly small. We need to find the most catastrophic events in the universe if we hope even detect them.
A supernova detonating asymmetrically, or two supermassive black holes orbiting each other, or a Galactus family reunion; are the magnitude of events we're looking for.
The most serious attempt to detect gravitational waves is the Laser Interferometer Gravitational-Wave Observatory, or LIGO detector, in the United States. It has two facilities separated by 3000 km. Each detector carefully watches for any gravitational waves passing through by the length of time it takes for laser pulses to bounce within a 4km long sealed vacuum.
If a gravitational wave is detected, the two observatories use triangulation to determine its magnitude and direction. At least, that was the plan from 2002 to 2010. The problem was, it didn't detect any gravitational waves for its entire run.
But hey, this is a job for science. Unbowed, the steely-eyed researchers rebuilt the equipment, improving its sensitivity by a factor of 10. This next round starts in 2015.