LUX is a "time projection chamber".
That means it is a big volume of material (in this case cryogenic xenon) and subjected to a strong electric field. The field causes ionization electrons to drift to two or more non-colinear planes of detection wires. The front wires must be so-call "induction" wires that do not absorb the ionization electrons.
This means that you can get information about the drift electron's positions in at least two different direction and reconstruct their position in two dimension.
But it gets better: with a uniform field the drift velocity is very reliable, so if you know when the electrons started drifting and when they were detected you also know how far they drifted and thus have reconstructed their starting position in 3D.
Heavy noble gasses make a really good medium for such devices because
If sufficiently pure loose ionization electrons can go uncaptured for many miliseconds allowing very long drift distances (meters).
These materials scintillate (that is release light) when ionizing radiation passes through them. That light is detected within nanoseconds of it's release and used to tag the drift start time. The electron detection electronics, of course, tag the detection time.
LUX is searching for ionizing events in the detector that
This post imported from StackExchange Physics at 2014-03-24 04:16 (UCT), posted by SE-user dmckee
Can not be explained by the (many) known kinds of physics that generate signals in these detectors
Have the characteristics that are expected of WIMP--ordinary matter interactions (which can be conjectured with some accuracy because we define a WIMP as having certain properties; basically there can only be elastic $Z^0$ at the WIMP vertex which generates a modest number of final states).