The movie features a Klingon who has taken control of the Enterprise, and has launched it for a one-hour flight with only him and yourselves (the skeleton crew) on board. After watching a few minutes of film to set up this situation, you will spend most of the time watching a star field passing by, and a clock timer. However, occasionally the Klingon will 'detect' you, in which case play stops. He will identify (and often insult) a particular player, often "the player who is moving now". He will then give instructions which will affect that player, usually negatively.
Also, some of the cards that players collect permit them to take certain actions only when the clock reaches a particular time.