Source: Wikipedia, "Starship 1", available under the CC-BY-SA License.
The object of Starship 1 is to destroy alien spacecraft while maneuvering through star and asteroid fields.
The game uses a first person perspective on a black-and-white monitor. The player's ship is controlled with a control yoke that is connected to two potentiometers. There is also a lever that controls whether the ship is moving "fast" or "slow". Compared to common arcade games of the time, Starship 1 was comparatively advanced, but used quite a bit of analog technology that would become less common in arcade games in following years.
As enemies appear onscreen, the player tries to center the enemy in the crosshairs and shoot it with his "phasors" by pulling a trigger on the control yoke. Alternatively, the player has 5 "proton torpedoes" per game that can be fired by pressing a large white button on the dashboard. This will destroy any enemy ship on screen, regardless of whether it is in the crosshairs (which are painted directly on the screen).
The enemy ships are roughly patterned after ships from the Star Trek: The Original Series and the title device from the 1967 episode "The Doomsday Machine".
The player does not view the game monitor directly; the monitor is recessed in the cabinet, and the player views a reflected image of the monitor in a half-silvered mirror with a space background.