Lunatic Pandora may have completed its journey, but so has Squall. Endure some chatter, watch some scenes and when you're in control of Squall talk to a man in white - Piet, and after his comrade comments on Rinoa, go examine her (she's off-screen to the bottom-left) to pick her up, then follow Piet into a room. Note the Save Point here, then go through another doorway to drop off Rinoa. Once done, exit by heading down to the return to the room with the Save Point.
Exit the room with the Save Point by heading right, then exit by heading up. In the next screen continue up past some stairs, then exit to the right to reach the control room, where you companion will babble before walking up to the front of the ship to look at the moon. Follow them to witness a scene, after which you'll be able to leave the way you came. Take advantage of this opportunity and go save your game at the room near Rinoa, as some very difficult games of Triple Triad lie ahead. While you're here, use Card Mod to get rid of every card say ones that are decent to play - ideally anything weaker than a Level 6 Boss card.
When you're ready, return to the control room and challenge Piet (blonde guy wearing white) to a game of cards. Fortunately Piet's not always the most troublesome of opponents, regularly fielding some of the weakest cards in the game, but the Lunar Bases's rules are... well, basically everything: Open, Sudden Death, Random, Same/Plus/Same Wall and Elemental. There's no way to avoid this, at least at first, so you'll just have to make the best of it, which means getting rid of any excess junk cards and paying attention to possible Same/Plus combos.
Although Piet won't offer to mix rules, if you play enough games with him a rule may randomly get abolished. You don't have to actually play him - just entering the game screen and quitting will work fine, although it may be tedious. If you get rid of Random or Plus, great! Same, Same Wall, Elemental and Sudden Death are all relatively trivial, while losing Open will actually hinder you. Honestly, just view this as a happy accident if it happens in your favor, we don't advocate spending the time to achieve a specific result here unless you're absolutely getting thrashed by a future opponent. With that in mind, it might be worth making another save just in case you accidentally abolish something minor and you need to go for a better rule.
Note: There's a general rule that Random is the most difficult rule to play with in this game, but in the Lunar Base, given the cleverness of the AI, Plus might actually be more annoying here. If you keep your deck trimmed down to Level 6 Boss Cards and better, Random should still see you ahead of your opponent in terms of card almost all the time, but Plus... the AI can plan moves ahead and counting... is for the birds. Just saying, it may be a better idea to get rid of Plus this time around.
If you've been following this guide and trim your deck down, Piet shouldn't be too hard. Just watch out for Plus and you'll be fine. Play Piet until he puts his Alexander Card up for play, and win it. Alexander isn't just a a top-notch playing card, with a 9 (top) and A (right) side, but it also can be turned into three Moon Curtain items via Card Mod. These will teach GFs the useful Auto-Shell ability, which is nice, but you might want to hang onto Alexander until you're done with the Lunar Base. Random rule and all. In fact, with a specific refining ability you'll be able to make Moon Curtains from store-bought items if you're patient... but this of course means you can't use Auto-Shell on your party until you acquire said GF, and you might just want Auto-Shell before then. Your call, but we opt to keep Alexander for now, then refine him into Moon Curtains and teach our GFs Auto-Shell when we're off the Lunar Base. You can always win Alexander back later, provided you completed the CC Group quest in Balamb Garden.
Note: If the players on the Lunar Base are just too difficult and your patience, cards and luck not up the task, don't sweat it. You can always win the cards again later provided you've completed the CC Group quest.
Exit the control room and you'll find yourself in the screen with some stairs. Save your game back at the room near Rinoa if you didn't do so after winning the Alexander Card, then head up the stairs near the control room. In here you'll find Ellone, your first opportunity to have an uninterrupted chat with her. Squander this opportunity by challenging her to a game of cards!
She'll field some pretty powerful cards, including Level 6 Boss Cards and she can be rather crafty if you left Plus intact. This will allow her to punch well above her card strength, which is saying something considering how weak some of the cards she'll field are. If you abolished Plus or Random, you might not have much of a time, especially if your collection of cards is lean in mean. Otherwise, Ellone's generally considered one of the hardest players in the game.
If you can, be sure to play her, as she's got the Laguna Card. Play her until she puts it in her hand, win it off of her, then pat yourself on the back for a job well done. You deserve it. The Laguna Card might not be the best playing card (hard to wedge it in safe corners), but it does refine into one hundred Hero items via Card Mod. Having a nigh inexhaustible supply of items that make you invincible for a short period of time can trivialize some fights, and is well worth refining.
The Lunar Cry
Win both cards and when you're done, save your game, then return to Ellone and talk to her. After the chat she'll follow you around; make your way back to the Med Bay - to Rinoa - and en route you'll see that... well, something's amiss. After some more chatter, Squall will find himself alone. Continue towards Rinoa to find out that she's awake! Or at least, mobile, but not quite herself. Running into Rinoa will cause you to be swatted away, so follow her to the control room (or rather, lead the way, as it'll go faster) and when you arrive Rinoa will get up to mischief. Try to interfere to get swatted away again, then after Rinoa leaves, stand by your companion to witness the moon continue to froth with monsters.
After this Piet will give you some more bad news. Leave the control room and head upstairs, and in the hallway leading to Ellone's room your attention will be drawn to the Lunar Cry. Just silly. After some more chatter enter a room near a fallen man, approach an airlock to the left to see Rinoa depart, then search a locker near the top of the screen to get Squall in some astronaut digs. Enter the airlock and try to fly after Rinoa, only for the way ahead of you to be sealed as some chatty astronauts approach. Backtrack towards the camera to return to the Lunar Base and return to the hallway outside of Ellone's room for more chatter. The president will be dragged away, literally kicking and screaming, charging you with looking after Ellone. So many damsels, so little time...
Return to the control room and talk to Piet, then watch some scenes where Rinoa causes more trouble. After Piet and your companion run off, talk to Ellone, then follow her down the elevator and another scene will play. Looks like you got your work cut out for you if you make it back to earth. If. When the elevators stops, use the Save Point to save your game, exit through a doorway to the right and talk to Ellone again, then take your place in the escape pod. Watch some more scenes, which supposedly show some endearing moments involving Rinoa, after which Ellone will finally get the past vision Squall wants to see. After getting the info Squall wants, talk to Ellone yet again to finally get on with things.
Well... sort of. A lot of melodrama and watching Rinoa floating around in space ensues, all so Rinoa remembers to press a button. Not sure how that's traveling to the past as much as it's ESP, but... whatever, it happened before with Laguna. Further abandoning any sort of plot consistency or physics, Squall will exit the escape pod - which was presumably speeding away this whole time - and you'll have to play a game of "catch Rinoa in space", which really just amounts to trying to get Rinoa's spinning body into the center of the screen. Ignore the timer, it really just tells you have much time you have until you reach - or pass - Rinoa, so this bit of gameplay mostly just involves scrolling right and perhaps down on the D-Pad/Analog Stick for a minute and a half, after which more chatter will ensue before Rinoa and Squall get one of the luckiest breaks in the history of gaming.
They'll board the red Estharan spacecraft that just happens to spin into them in a perfectly harmless manner and use the Save Point when you're back in control.