At first sight, it looks a bit like an updated and slimmed-down TFG Star Fleet Battles, which is not too surprising considering that Agents of Gaming got their start doing SFB supplements. Much of the similarity is just due to the subject - you could just as easily compare it to any number of tactical naval games. Most turns you probably won't need to do anything - there's a default allocation that provides all the power that the engines, weapons, and other systems require. You can power down some systems to provide more power to others, and you may have to power down systems as a result of reactor damage, but usually it takes care of itself.
Movement is semi-Newtonian, which is pretty close to the way things look in the TV show.
Ships have a thrust allowance rather than a movement allowance, and will travel in the same direction at the same speed indefinitely unless they spend thrust points to alter either direction of travel or speed. Movement is along hexrows, and the cost in thrust points to change direction by 60 degrees and the number of hexes that must be travelled between direction changes are proportional to speed. Ships must move a number of hexes equal to their speed each turn, and spend thrust points to change their speed before movement. Ships may face in a direction other than the one in which they are travelling, but can only use thrust if they are facing in the direction of motion or directly opposite it. Not true Newtonian movement, but close enough to be interesting.