This description of the Horizontal Gaze Nystagmus test posted by California DUI Lawyer.

Smooth pursuit is commonly described as a marble rolling across a smooth pane of glass. An example of lack of smooth pursuit is that same marble rolled across sandpaper. The officer is instructed to check both eyes, starting with the left eye first by moving the object to the officer's right. The object must be moved smoothly, at a speed of about two seconds to bring the suspect's eye as far to the side as it can go. Any choppy, shaky or fast hand movements by the officer may induce a nystagmus in the suspect's eyes and invalidate the scoring and test. 

The stimulus is then moved across the subject's face, checking the right eye and moving the stimulus as far to the side as it can go. Movement of the stimulus should take approx. two seconds out and two seconds back for each eye. This procedure is repeated.  Each eye must be checked with two or more passes. This is to insure that one is absolutely certain they are seeing a nystagmus. Once this clue is observed, the suspect is assessed one point for each eye that a lack of smooth pursuit is observed. The mere fact that this clue is seen in one eye, is no guarantee that it will be exhibited in the other eye. This is considered the easiest clue to see.

The eyes are then checked for Distinct Jerkiness at Maximum Deviation . The stimulus is moved to the side until the left eye has gone as far to the side as possible. At maximum deviation, no sclera or white will be showing in the corner of the eyeball. The officer must hold the eyeball at that position for a minimum four seconds, and observe the eyeball for distinct jerkiness. The jerkiness must be both distinct and obvious.