You can find the game manual online here: https://segaretro.org/index.php?title=File%3AStar_Trek_The_Next_Generation_The_Advanced_Holodeck_Tutorial_GG_US_Manual.pdf&page=1

The game's missions are fairly random, so there's no real strategy to use. Much of your run will depend on the luck of the draw. For example missions that involve fighting other ships will generally take longer than rescue or transport missions. Ship battle missions will also take more time because you may need to effect repairs.