The two stages are 1) the acquisition of the opponent's fecal matter by rectal finger insertion and 2) the smearing of the fecal matter on the upper lip of the opponent (the moustache).
There are no rules regarding physical conduct (save the completion of the two stages), but causing the death of the opponent is strongly discouraged. A struggler must first acquire fecal matter from the opponent by forcefully inserting a finger (usually the index finger) into the anus of the opponent. The sullied finger must then be applied to the upper lip of the opponent before the opponent does likewise.
An extension of the moustache struggle involves a group of strugglers (3 or more). A group moustache struggle is highly unpredictable because an opposing struggler may strike at any time. For example, if two strugglers are engaged in the final throes of stage two, a third struggler may sneak up unawares, perform a very fast insert-and-wipe maneuver, and usurp the match.