Alright, now for how the game is actually played. This might seem to be a bit out of order, but I'm going to skip the character selection and setup for now and just hit the actual game turns.
Every character takes their turns in order, though discussion of what should be done and such during each player's turn is encouraged. The first thing you do is draw skill cards into your hand based on your character card. Using Starbuck who I posted above as an example, She would draw two cards from the Tactics deck, two cards from Piloting, and choose between Engineering or Leadership for her final card. If a player has revealed themselves as a Cylon, they instead draw only two cards, but they can pick from any decks to draw from.
The second step of the turn is movement. A Human or unrevealed Cylon can move to any space on Galactica or Colonial One. If a character is a pilot and is piloting a Viper, they may also choose to move to an adjacent sector of space. If you choose to move to a ship that you aren't currently on, you must discard one of your skill cards to make the move. Keep in mind that there are ways to get actions even when it isn't your turn, so even if you don't plan to use a location's special ability, it may be worth moving to one that you could use if you needed it later on a different turn.
Third is the Action step. You get one action on this step to use. Most locations have an ability that you can choose to use with your action. Some skill cards also have an ability that you can choose to use with your action. Some of the characters' Once Per Game actions require you to use an action to activate them. If you are piloting a Viper, you can use your action as an additional movement or you can attack an enemy ship that is in the same section of space as you are. Attacking an enemy ship requires a die roll and the result required depends on what ship you are attacking. There is a chart on the last page of the rulebook. Revealing yourself as a Cylon is also an action.
If you are a Revealed Cylon, your turn ends after this step. Humans have three more steps, however.
The fourth step is the Crisis step. The top card of the crisis deck is drawn and resolved. There are three types of Crisis: Cylon Attack, which puts more enemy ships on the board and has them moving and attacking; Skill Checks, which I will cover in more detail after the turn order; and Events, which are simply picking an option off the card to occur.
Fifth is the Activate Cylon Ships step. Most Crisis cards have a picture of a Cylon ship on the bottom left. That type of ship will take an action depending on the current state of the game board, which I will go into more detail on later.
The final step in the Human turn is the Prepare for Jump step. If the Crisis card has a jump icon on the lower right, the Jump Preparation track is increased by one.
Once the final step in a player's turn has been completed, the next player starts their turn from the draw step.
Before I explain skill checks, I'm going to explain the Destiny Deck as it's used in these checks. At the start of the game, two random cards are taken from each of the skill decks and added to the Destiny Deck, which is then shuffled. If the Destiny Deck is depleted, it is rebuilt with two new cards from each stack. Every time a skill check is made, two of these cards are added to the check. I'll explain in more detail in a moment, but each skill check has skill types that are positive, and skill types that are negative. Since the Destiny Deck can add any type of skill card, it can help or hinder the checks, or simply cancel itself out.
Skill checks can be activated from certain locations or from Crisis cards. The picture below is an example of a Skill Check on a Crisis Card.
I apologize for the tiny text but you should be able to see enough to understand the explanation. During the actual game, if I can't find larger images I'll type out the information so it's readable.
The top of the card has a number on the left and the title of the card. The number is the total number that the skill check has to add up to for it to be considered a Pass. In this case, the target number is 8.
On the left of the card, next to the picture, is a set of five boxes. These represent the five types of skill cards. If a box is colored in, that type of skill card is positive for this check. If it is not, that type of skill card would count as negative. From top to bottom, they are Politics(yellow), Leadership(green), Tactics(purple), Piloting(red), and Engineering(blue). For this check, Politics and Leadership cards would be positive, and Tactics, Piloting, and Engineering would be negative.
The box directly below the picture is just flavor text. Below that, there is a box that has the possible results for the check. Some checks, like this one, have a Partial Pass which is shown as a number between Pass and Fail in the results box(in this case, the 5+). If the skill check total ends up as a Pass, the Pass effect happens. In this case, that is no effect. If the total is lower than the Pass but high enough to trigger the Partial Pass, then that effect occurs. With this card, one morale would be lost. Finally, if the total result is lower than the partial pass result, or lower than the check result if there is no partial pass, then the Fail condition occurs. For this example, the Fail condition on this card is that one morale is lost and whoever has the president title must discard four skill cards from their hand. For locations, which don't have a failure effect listed, the failure effect is simply no effect.
When a skill check begins, two cards are added to the check from the Destiny Deck. After this, the players play into the check face down. You are not allowed to tell other players what you are adding to the check. You can give a rough idea, such as saying your cards are low or high, but you can't say which skill type they are or any specific information about the strength. Normally cards have to be played in turn order. For speed of play with an online game, this will normally not be enforced, but it can be if the players wish it to be or if the Investigative Committee card is played, which makes players play into the check face up instead of face down. Once all of the cards have been dealt in, I will total them and tell you what has been played in(not the order in which they were played, though, I will sort them by type and strength so you can't tell who played what) and the end total of the skill check.
When deciding whether to attempt a skill check or to hold cards and deliberately allow it to fail, the players should keep in mind how many characters draw positive cards and roughly how many cards they could have. Remember that players only draw their five cards during their own turns, so if the same requirements keep showing up, they could run out of cards before they get a chance to draw more. Also, keep in mind that the decks have a lot more of the smaller cards than they do of the larger ones. Each skill deck has 8 copies of the card with 1 strength, 6 copies with 2 strength, 4 copies of 3 strength, 2 copies of 4 strength, and one single card with 5 strength.
During the Activate Cylon Ships step, if there is an icon in the lower left of the crisis card(which there is on the example above, to activate Heavy Raiders), that type of ship is activated. I will handle the actual activation, but it would be useful for you guys to know what they do. There is a quick reference guide on the last page of the rulebook that explains what Raiders and Heavy Raiders do if they activate. There is also a Launch Raiders activation which causes three Raiders to be added to the board for each Basestar in play, and an Activate Basestars icon which causes any Basestars on the board to attack Galactica.
Finally, there is the Prepare for Jump step. If the crisis card had an icon in the lower right(which the example card above does), the Jump Preparation track in the upper right area of the board moves one space to the right. If the track reaches Auto Jump on the right, then the fleet jumps. When the fleet jumps, all ships(enemy and ally) are removed from the board. If a player was piloting a Viper, they are moved to the hangar bay. The admiral draws two cards from the top of the Destination Deck and chooses one of them. The second card is placed on the bottom of the deck. Nobody but the Admiral gets to see what the second card was. The instructions on the chosen card are followed, and the card is set off to the side of the board. Each destination card has a number on the bottom, from 1 to 3. In order for the humans to win, the total distance on played destination cards must total 8 or more and the fleet must make a final jump(which does not require a new destination). Once the total number reaches 4 or above for the first time, the Sleeper phase begins and all players are given a second loyalty card.
If you look at the track on the board in my previous post, you will notice that the first space is black, then there are two red spaces, two blue spaces, and the Auto Jump space. The black one is actually the start space, the token that shows how far you are along the track is black. When the token reaches the blues spaces, a player can cause an early jump by using an action in the FTL control location, but must risk population to do so. On the first blue space you are risking three population, and on the second blue space you are risking one. When you attempt this you roll a d8, and if the number is 6 or less, you lose that amount of population. If the roll is 7 or 8, you do not lose anything. Either way, the rest of the jump is handled the same way as an auto jump.
That pretty much does it for the very basic game turn. There are a lot of other rules that can come up, but generally aren't handled every single turn. Like I said before, if people are interested in actually playing I suggest you run through the rules/errata on your own. Much like Arkham, this game is fairly complicated but once you get the hang of it things are fairly smooth.