The primary purpose of airborne laser altimetry is to determine the ellipsoidal or geoidal coordinates of a series of points on the surface of the Earth. An aircraft that is instrumented with a laser altimeter, an inertial navigation system, and a Global Positioning System (GPS) receiver provides the following data: (1) laser range to the Earth's surface, (2) measurement platform spatial location and orientation, and (3) aircraft kinematic trajectory in ellipsoidal coordinates. These data are sufficient to determine (georeference) the three dimensional coordinates of the points where the beam from a pulsed laser intersects the Earth. We develop the exact equations necessary to georeference the laser points. We also discuss calibrating the laser pulse timing, laser positioning and alignment relative to the local-level reference frame, correcting atmospheric refraction effects on the laser pulse, and time synchronizing the various data streams. We use a laser altimeter mission flown over Lake Crowley in California to demonstrate our methods. For seven passes over the lake, our heights agreed with a local tide gauge at the Lake Crowley dam to better than 10 cm with standard deviations ranging from 1-4 cm. The horizontal accuracy of the georeferenced points is still problematic; we have no three-dimensional control points that the laser has hit. Geometrical considerations indicate that the measured horizontal location of the laser footprint is within two metres of the true location when the aircraft altitude is less than one kilometre above the local surface.