Gravity waves are expected to make thing slightly longer and shorter as the wave travels at the speed of light.
To see this, take two rulers and place them at 90 degrees to each other.
If a gravity wave comes along that is parallel to Ruler A, it will make A get shorter then longer while Ruler B will get longer then shorter.
So you should be able to see a gravity wave by continuously comparing the lengths of these two rulers.
Unfortunately these changes in length are predicted to be very, very small, so you need really, really long rulers to make the total length difference be a detectable fraction of the wavelength of light.
(This is a lies-to-children explanation. Everything I just said is more or less wrong, however it's sort of close.)
GEO600 is using rulers 600m long, and LIGO in the USA has rulers 4000m long.