Back aboard the Celsius, speak with Shinra, then head to the Cabin to shop and rest if you need it. (Even if you don’t, go somewhere.) Return to the bridge, then head to the deck for another scene. (If your completion percentage isn’t over 70%, you won’t see one.) You’ll get an Al Bhed Primer after, then head to the Cabin for a scene, only viewed if your percentage is over 80%. Then head to the bridge, cabin, bridge, and deck in that order to meet up with Rikku for another scene, only viewed if your percentage is 95%. (That means you’re perfect so far.)
Next, head to the Farplane Abyss via all five routes: that means Besaid (the earlier walkthrough), Kilika, Djose, Bevelle, and the Calm Lands. Each is easy enough to navigate, though Djose gives you a stone-pushing puzzle. In it, push the leftmost stone towards number two, the rightmost towards number one, the middle one towards number two. By doing all five routes and getting to the platform where you fought Dark Anima, you’ll get a scene and the Megiddo Flame Garment Grid (which allows you to use Ultima!).
That’s about it. Be sure you’re ready for the rest of the game, and throw yourself headfirst back into the Abyss.