About the working of LIGO How is it that the gravitational wave occurred exactly so as to compress one tunnel and expand the other one( as is inferred from the explanations they Caltech gives)?
Or is LIGO built in a way that all gravitational waves will cause this effect? Can you elaborate on this if it is so?
 A: Gravitational waves are transverse waves. That means if the source of the waves is at some distance in the x-direction, you get the best effect by aligning your interferometer arms in the y- and z-direction.
Since the gravitational waves can come from any direction you theoretically would get the best results if your interferometer had 3 arms - 2 perpendicular to each other on the ground and one pointing upside (or down), then you would get an effect on at least 2 of the 3 arms, no matter from which direction the wave is coming from. Then it would also be easier to triangulate the exact position of the source.
Practically you can only cover 2 axes per location, because it is not possible to build a 4 km hight tower, but in the worst case you still get the effect on at least 1 of the 2 arms (if the wave source is located in the x-direction and you have the arms aligned on the x- and y-axis you still get an effect on the y-arm).
Therefore one builds more detectors located on different positions on the globe. If you have a 2 arm detector at longitude 0° and one on longitude 90° you can have x, y and z covered. 
A: This is seen simply in the animation from wikipedia


The effect of a plus-polarized gravitational wave on a ring of particles.

It shows the way space is distorted by how a ring of particles would behave as the wave passes. It is seen that a detector with two arms ( L shape) measuring the diameters of the ring , would get a maximum effect by the arms being in a perpendicular direction to each other.
The LIGO arms  by being perpendicular measure the space distortion at a maximum possible geometry. Think of a detector in the animation to measure two perpendicular distances,  the signal would fit the same function whichever way it was oriented to the detector. 
