Squall starts out disc 3 lying in bed, wondering at the events that recently transpired, after which he'll go mope over a comatose Rinoa. Fortunately he's interrupted by Quistis, who directs him to Edea's orphanage, where the sorceress has apparently retired to after your last battle. Just go up to the bridge, talk to Nida to take off, form a party of three, then immediately land the Garden. You fought Galbadia Garden near the orphanage, so it should only be a short walk to the southwest. Before bothering with that, however, let's turn our attention to that new Alexander GF you should have drawn from Edea a moment ago...
GF - Alexander
Possessing only Spr-J, Alexander isn't much of a GF when it comes to boosting your stats, which is fine considering that you've long since had all the common stats covered. More interesting is Alexander's Med Data ability (which doubles the potency of "medicine") and the subsequent Med LV Up ability, which allows you to upgrade lower-quality healing items into higher-tier ones. High Mag-RF will also allow you to acquire high-level spells (Blizzaga, Curaga, Firaga, Thundaga, Tornado or Triple) by upgrading mid-level spells (Blizzara, Cura, Fira, Thundara, Aero or Double, respectively).
The real winner here is obviously the stocks of Triple, if you somehow didn't managed to get any earlier. You can refine Grendel cards to score Dragon Fins (or you can get Dragon Fins directly from Grendels - either via drop or Mug), which can in turn be refined via Mid Mag-RF (a Quezacotl ability) into twenty Double spells. Finally use High Mag-RF to turn these Double spells into Triple. It's not quite as quick as drawing Triple from Cerberus was, but it's another avenue, one well worth pointing out.
Where does Alexander go, all things considered? Well, depending on your previous actions this GF may not matter much. If you refined the Selphie Card into Elem Guard items and used those to teach GFs the Elem Def-Jx4 ability, you probably won't be all that impressed by Alexander's own Elem Def-Jx4 ability. If you don't already have three GFs with Elem Def-Jx4, however, then junction Alexander to the Ifrit-user. Likewise if you didn't get Rosetta Stones in the D-District Prison earlier, the Ifrit user still needs Ability x3, which Alexander also has. We junction Alexander to this character regardless.
With that taken care of, enter the orphanage on the world map, pass through a doorway and in the room beyond you'll encounter Cid, who makes light of his failings as a leader and the impossible situation he was in earlier. What a tool. Grab the copy of Timber Maniacs #11 on the floor along the eastern edge of the house, then follow Cid through the remains of a doorway to get outside. Approach him and Edea to provoke more chatter and after Edea stops chatting momentarily, challenge her to a game of cards. Yes, really.
She uses the Centra/Winhill ruleset, which if you abolished earlier will make this part a breeze. If not, the Centra/Winhill rules are fairly brutal: Random and Same/Plus. Do your best to win the Edea card from her, which is just a fantastic playing card, having A-strength sides on the top and right. As for Card Mod, she refines into three Royal Crown items, which you hopefully don't need anymore. Even if you could find some use for them, you can refine them from store-bought items shortly, so spare the Edea card for playing.
Once that card is yours, Edea will explain why she... you know, tried to kill you repeatedly. Two names pop up - Ultimecia and Adel, two sorceresses who, together, can be a dire threat to you and everything you hold dear. Eventually Edea will start to repeat herself, which signifies Squall has stopped paying attention to the fate of the world. Walk away from Cid and Edea to move the conversation along, where Squall whines about Rinoa and Cid has the gall to lecture you about leadership. Long story short, Squall is a terrible leader, Cid was even worse, but somehow you've got to keep this Ultimecia from getting her hands on Ellone. Fun.
Weapons Mon Jul and Combat King 003
When you're back in Balamb Garden, endure some more chatter, ride the elevator down to the 1F lobby. To move things along you'll need to talk to Rinoa, but before you do, head into the Training Center, and on the first screen head up and to the left to then next screen, then work your way left around two fallen trees, beyond which you'll find an issue of Weapons Mon Jul on the right side of the metal walkway. This magazine teaches you the Twin Lance, Rising Sun, Ulysses and Crescent Wish weapons, if you still need such recipes.
Leave the Training Center and if you want to get one more magazine before pressing on with the game, there's a bit of running around you can do. It honestly may be easier to just play on ahead and buy it shortly, but... well, if you'd prefer to hang on to a few trivial Gil and get it a bit earlier... Anyways, make sure Zell is in your party, enter the library and talk to a girl on the first screen near some bookshelves. More specifically a "Library Girl with a Pigtail", who will get flustered when Zell talks to her. There's no accounting for taste, eh? Zell and the girls on the Library Committee could have had a series of interactions running throughout much of the game, but it was all fluff and none of it needed to be completed until now. In fact, the only noteworthy bit involved bringing Zell back to Balamb during the missile crisis to score a better gift - a Mega Phoenix - from this very same girl.
Anywho, return to 3F and bid Nida fly, then travel back to the city of Balamb and when you enter, look out for a girl in a red skirt on the gas station screen. Talk to her and she'll mention "a girl at the Garden with a pigtal", who apparently visited Zell's house. Head over to Zell's house and Zell will talk to Ma Dincht, who won't confirm the visit by the pigtailed girl. Weird. Visit the inn and sleep for the night, and when you wake up Zell will be gone. Head downstairs and you'll see Zell talking to the pigtailed girl in the lobby of the hotel, after which he - and by extension, you - will acquire Combat King 003. This will teach Zell the Meteor Barret limit ability... not that you'll need it, given it's more effective to spam Booya and Heel Drop.
With that done you'll need to go find Rinoa in the Infirmary, but you still have some freedom to do what you wish if there's anything you want to finish up. If you didn't get the Tonberry GF yet, consider heading to the Centra Ruins to do that now. If you had trouble winning the Edea card, you can travel around and abolish rules from Winhill to make the task easier. Finally, you can always head back to the Kashkabald Desert and kill Cactuars if you want to score some AP for your new GFs. It certainly can't hurt to learn Cerberus's ST Def-Jx4 or Alexander's Elem Def-Jx4, among other abilities. The less you leave undone, the better - much of disc three will force you to pursue the story, and when you do get your freedom back you'll have quite a few new thins to do. Odin, however... you can keep ignoring that guy if you wish.
When you're ready to move on, visit Rinoa at the Infirmary and Ellone will clearly get up to her old mischief again, as you fall into another Laguna dream.