In The Cage, in Where No Man has Gone Before, in The Corbomite Maneuver, and in The Man Trap, there was absolutely no explanation given about things like transporters or warp drive. Ditto for Encounter at Farpoint, Emissary, Caretaker, and Broken Bow, and for all the theatrical films. In The Making of Star Trek, the rationale was given, and it was to the general effect of "Does Sgt. Friday go into a protracted description of his revolver when he pulls it out?"
Many of the theatrical films, as well as the opening episodes of the last 4 television series, did go into some detail on how the characters were brought together (or reunited), but what was at the time (and arguably still is) the theatrical film that was the most accessible to non-fan audiences (The Voyage Home) did practically none of that, and simply assumed that the audience would either already know the backstory of Kirk, Spock, et al. being on Vulcan, in a stolen Klingon scout ship, with Spock still in the process of recovering his marbles, or would go along for the ride, and let the story pull them in.
Many of the theatrical films, as well as the opening episodes of the last 4 television series, did go into some detail on how the characters were brought together (or reunited), but what was at the time (and arguably still is) the theatrical film that was the most accessible to non-fan audiences (The Voyage Home) did practically none of that, and simply assumed that the audience would either already know the backstory of Kirk, Spock, et al. being on Vulcan, in a stolen Klingon scout ship, with Spock still in the process of recovering his marbles, or would go along for the ride, and let the story pull them in.
