One player or team deals, and the other player or team plays first card. The first card played must be a Planet or Moon, which is laid face up in front of the player. The other player can take an opponent's cards (Planets and Moons) by playing a Comet of equal or higher value to a Planet or Moon, play a Planet or Moon themselves, or pass. (they can also play a trump - see below). Note that a Comet can only be played against a single Planet or Moon card, not multiple ones!
Play continues until the deck has been exhausted no further cards can be drawn. When the last card is drawn from the deck, players continue until their hands are expended or until they reach an impasse (such as both players having nothing left but Moons and/or Planets). Points are then tallied.
Trump - if a player plays a Nova (trump card), they take ALL planets and Moons on the table - including their opponents and their own. This is the only case where a card can take multiple cards.
For terrestrial players who want to play Starbuckaroos:
Moons = Clubs, Planets = Spades, Comets = Diamonds, Novas = Jokers
Might be an entertaining diversion if your SF PC's gamble, as some local/background flavor, or something : )