You regain control of Tidus in the passenger quarters. There's a chest half-hidden behind the group of Besaid Aurochs that contains a Hi-Potion. Exit through the door and talk with O'aka a few times, and he'll ask you to lend him some more Gil — do so (101 is enough). Ignore Dona and Barthello and head up to the deck of the ship. Retrieve Al Bhed Primer Vol. V in the steering room, then head to the end of the ship to witness a scene between Tidus, Yuna, and some of the Luca Goers. Speak with Yuna and then go up the stairs to the balcony. You'll overhear Lulu and Wakka speaking about Tidus. You can climb the stairs multiple times to see some scenes which serve no real purpose other than to enrich the story a little.
Obtaining the Jecht Shot
It's important that you save here and now before doing anything else. The Jecht Shot will greatly help and acquiring it sooner rather than later is best, so you really want to retry if you mess up. Head onto the front of the ship and approach the blitzball laying there. Tidus is obviously still moping over his father, and you'll get another flashback. Time to prove Jecht wrong! The on-screen instructions are self explanatory, but basically you want to hit and a specific directional button at the same time as Jecht's insults show up on the screen. If you don't manage it (you'll know because Tidus will miss the ball when he spins to kick it) then reload, either by resetting the system or using Square's handy soft reset (+++++). If you manage it you'll have the Jecht Shot at your disposal in Blitzball matches from now on. You'll soon see why it's important soon enough.
After the scenes and talking with Wakka and Yuna you'll rest. You'll be prompted to save — do so if you want, and afterwards, you'll be sailing into Luca!
After you control the Airship, return to Killika Port and take the boat to Luca again. On the top level of the ship, there's a guy studying Spira's animals who will ask you how many seagulls are flying around after you talk to him enough times. Count how many there are from every view on deck. Answer correctly (11), and he will give you Wakka's weapon Ace Wizard, equipped with the first four levels of Magic +%'s.