At the start of the game, players are randomly assigned an alien power and are given five planets in a star system, or hex, each with four tokens (or ships) on it. These tokens represent your military forces or the ilk; basically, what you attack and defend with. You'll also be dealt a hand of 7 cards, which will either be Challenge cards (which, in turn, are either Attack cards or Compromise cards) or Edicts. Challenge cards are used in challenges, whereas Edicts have a lot of possible uses and I'll go into them later but first other stuff. I'll then randomly select a player to go first, and then we'll begin.
A turn is usually composed of one or two challenges, and each challenge has a series of steps to it. Firstly, at the start of the challenge, if a player has any tokens in the Warp, he may (and probably should) take one and put it on any base he already has. He then flips over the top counter in the Destiny Pile and then has to attack the relevent player shown, by aiming the Hyperspace cone at one of the planets on that player's Hex. If a player gets his own colour, he can attack a single foreign colony on one of his own planets, or draw a new counter. In either case, the player becomes the main offensive player, and the target of the attack becomes the main defensive player.
Once the Cone has been put into place, the offensive player may take between one and four shipss from anywhere he has them, as long as he leaves at least one in each base, and puts them on the top bit of the cone. Both players then have the chance to ask for allies; firstly, the main offensive player asks as many people as he wants, including none if he so wishes, to ally with him. The main defensive player may then do the same, and can ask players asked by the main defensive player if he wants to. All players invited to ally then have the chance to accept (and choose a side if asked by both), and can provide between one and four shipss towards their side of the battle. Offensive allies go to the top of the cone with the main offensive player, and the defensive allies go to the little ring on the cone.
Both main players then choose one Challenge card from their hand and would place it face down in front of them. Because this is the internet, we'll settle for they just PM me the card they want to play. I'll then reveal both cards and at that moment in time a whole load of shit can happen so if you'll just bear with me I'll explain as much as I can as quickly as I can.
Firstly, the most likely scenario is that both players play Attack cards. You'll notice that all Attack cards are just a big number so nobody can miss it. In in-game terms, an attack card is "We're going to try to blow the everloving shit out of you", so if both players play attack cards we have a fight on our hands. They are pretty quickly resolved, though, with a quick bit of addition; the total power of a side is the sum of the number on its card and the number of ships fighting for that side. The side with the bigger number is the winner. If the defense wins, then all the attacking ships are sent to the Warp and the defensive allies get one reward for each ship they sent in (either a ship back from the warp, or a card) and return their ships, and that's it. If the attacking force wins, all defensive ships (allies inclusive) get destroyed and all attacking ships are placed on the newly vacated planet.
Another possible scenario is that both players have played Compromise cards. If this is the case, then all ships go back home and twiddle their thumbs, and the main players have 72 hours to negotiate a deal amongst themselves. A deal can involve the trade of cards and/or allowing the other player to establish ONE base where you already have one (your own planets count). You can also promise to do something, but there are no requirements for promises to be kept at any point. I'll accept a deal to be made when there appears to be a sensible agreement on the table. If 72 hours pass, or one player juts flat out refuses to agree to a deal, then it collapses and both involved parties lose three ships to the warp.
And finally, we could have a situation where one player wants to Compromise and the other wants to Attack. Think about it logically; if one person wants to talk and the other wants to blow something up, who's going to win in an intergalactic war? The player who played the Attack card automatically wins and gets the colony/the allies get the bonuses, and the compromising side gets blown to the warp. However, attacking a defenseless fleet is looked down upon in intergalactic politics, and so the player who played the Attack gives compensation in the form of one random card from his hand for every ship from his opposition's main player that he destroyed. Allies get nothing but death.
After all of that happens, the challenge cards are discarded, and if the offensive player was successful, either by means of destruction of the opposition or a successful compromise, then he has the option of attacking again. However, he can only do this if he still has a Challenge card in his hand. He can also decline the second attack if he so chooses. If he's already made a second challenge, then that's the end of his turn and play passes to the left. I should probably mention at this time that if you are on your first challenge, or are being targeted as part of one, and you have no challenge cards in your hand, then you must discard your entire hand and draw a new hand of seven cards.
Play continues as such, with constant challenges, until there comes a point where a player has managed to gain 5 foreign colonies (bases that aren't on his hex). Whenever this happens, the player who has done so is the winner. Wow that was simple what have I forgotten oh I know the Edict cards and alien powers. Firstly, the latter. Remember at the start when I said each player is given an alien race? Well, each race has a power attatched to it, and that power has the ability to screw the rules. I'm not going to go into them in this spoiler, check the next one. However, if you are in a state such that you have 2 or less bases on your hex, you lose your power until you can get 3 bases.
Edicts are a little more easier to explain because they have less caveats to them than the alien powers. Each of them can turn the tides of the conflict if used at the right time, and for that reason are extremely powerful and rare - there are, for the most part, only one of each flare in a deck roughly 80 cards big. Edicts can only be played when the card says they can be played, and are one shot things-once used, they are sent to the discard pile. Not gonna tell you what they are, though, because I'm a heartless bastard and if you really care that much look it up yourself.
In case I've missed anything here's the full rulebook:
http://daveola.com/CosmicEncounter/Rules/Eon.Rules.pdf Just note that we're playing a reduced version than the book, we're basically playing sans expansions.