After landing, head northeast to see Maester Mika debark.
Lulu shows up after your blitzball tutorial and takes Tidus to look for Auron.
Go down the stairs to the left of the ones going up.
Get the 2 Hi-Potions from the chest and pickup the Al Bhed Primer VI behind one of the players on the left.
Go back out and down the stairs.
Take the left path to circumnavigate the stadium in a clockwise fashion.
On Number 1 Dock you can get 600 gil and a Tidal Spear.
You can also meet O'aka here who will actually sell you stuff now.
On Number 2 Dock you can get 2 Phoenix Downs in the chest there.
On Number 5 Dock there's a Magic Sphere and HP Sphere hidden behind the crates in the back.
When you get back to the stadium entrance, head south.
Head east from the bridge to reach the Square.
From there, take the stairs on the right.
Get the 1000 gil in the chest and then go back down and into the bar at the north end of the square.
After Yuna's disappearance, Tidus, Lulu
and Kimahri will have to track her down while Wakka plays blitzball.
Go back to the stadium and head left.
You'll have to battle some Workers on the way.
When you reach the Al Bhed ship, you'll have to fight Oblitzerator.
Afterward go to the locker room and talk to Wakka to start the blitzball against the Goers.
After the game, Tidus and Wakka will be
attacked by a number of Sahagin Chiefs while in the sphere.
Then you'll be in control of Auron and must defeat a Vouivre.
After that all 3 must fight a Garuda (Luca) together.
Follow Auron to where the others are waiting.
Talk to Yuna and you'll be free to go your way with Auron now a member of your party.
Go back into Luca and visit the Theater to find the Al Bhed Primer VII