Luca is one of the biggest cities in Spira, so obviously there's a lot to do here.
Meeting Maester Mika
After watching the handful of scenes and seeing Tidus make a fool of himself, follow the red arrow around to the next dock. Move towards the actual dock section and you'll be introduced to Maester Mika and Maester Seymour. Afterwards you'll be prompted to save your game again — do so, unless you feel like sitting through those chain of events again and again if you lose the Blitzball matches that are coming up.
You'll then be in the Besaid Aurochs' locker room. Wakka will enter a short time afterwards and tell you that's you're up against the Al Bhed Psyches first, and since you were seeded, you only have to win one more game after that to win the tournament! Now you'll get the game's Blitzball tutorial, but since this is quite long you can skip all of it if you're familiar (It'd be wise not to if this is your first time through, though). Yuna will enter after, and you'll leave to follow her. Head down the steps and save your game again if you want, then head right (ignore the red arrow for now).
Finding Sir Auron
Go right to the Number 5 dock until you're facing a set of metal crates. If you look to the right and on your map there's a gap to your right — go through and you'll find yourself in a hidden area with two chests containing a Magic Sphere (creates a Magic +4 node on the Sphere Grid) and a HP Sphere (creates a HP +300 node on the Sphere Grid). Now go back and up (the opposite way from the red arrow). Go around the next dock in this manner, since there's nothing in it. When you get to the Yevon ship, begin to follow the red arrow again.
You'll arrive back at the dock with the S.S. Winno — along the dock a short way is a chest containing Phoenix Down x2. In the next dock around, you'll find O'aka again — lend him some more Gil (101 is enough, but feel free to lend him however much you want). He also actually has more to sell now — his equipment is half decent but the chances are it's going to be a little too expensive for you as everything costs at least 1,100. It's a good idea to refrain from buying the Stunning Steel for Tidus because 3,000 Gil isn't worth it. Some items are a good idea to buy though. Anyway, check along this dock to find two chests, one containing 600 Gil and the other containing a Tidal Spear for Kimahri.
Now go back to where you started at the front of the stadium. Enter the Locker Room on the left side, which is locker room B. There, you can find Al Bhed Primer VI and a chest with 2 Hi-Potions. Now, you can simply follow the arrow. If you head back a short way after you catch up with Yuna you can head on up to Luca Theater to collect the Al Bhed Primer VII in the reception area. You can pick up 1,000 Gil if you go right instead of straight into the cafe, as well as meet Luzzu and Gatta again. Follow the arrow as you did before and you'll enter the cafe, and find that there is no Auron in sight. Who would have thought it? A bar brawl in a Final Fantasy game? Kimahri participating?
Anyway, you'll be in Luca Stadium afterwards, watching the Blitzball arena being set up, Mika's official starting speech, and the Aurochs swimming out into the sphere pool. Oh dear, Yuna's been kidnapped! Anyway, Lulu's told you everything you need to know, so follow the red arrow to the Al Bhed boat. You'll come up against a pair of Al Bhed Worker machina — they aren't too difficult. Physical attacks from Kimahri and Tidus and Lulu's Thunder will destroy them pretty quickly. Move through the next dock and you'll be confronted by another pair of Worker machina — the same tactics apply. In the next dock you'll have to fight three pairs of Al Bhed machina, so to speed things up have Tidus cast Haste on Lulu. After this battle, you'll see Wakka in the sphere pool again, and get an opportunity to save using the Save Sphere. Make sure you do, there's a boss coming up.
Approach the ship and you'll jump on it. What's that‽ That's a little bigger than a Worker machina…
Boss Battle: Oblitzerator
Tidus will mention at the start of this battle that there's a crane you can use. His trigger command is "Use crane" so to start off the battle, do so. It won't work. Lulu will comment on it being out of power. Hint anyone? If you attempt to use it three times then Tidus will basically tell you what you have to do — use Thunder on it three times to power it back up. This is the easy way of fighting this battle — there's a harder one.
The Oblitzerator's main attack is Blitzball Rush, which is 8 or so random hits on your part for about 35 damage apiece. It's weak to thunder, but it'll counter magic with Mute Ball which inflicts 100 damage and Silence, and it'll counter physical attacks with Blind Ball which inflicts 100 damage and Darkness. Soon you'll realize that your entire party can't do anything. Before this happens, just use Thunder on the crane three times and then have Tidus use his trigger command again. The crane will hover over the Oblitzerator, then…wrench it in half. This will deal a little over 90% of its remaining health to it, and now it can't attack you or counter anything. Finish it off to save Yuna! After you properly regain control of Tidus just follow the red arrow back to the Aurochs' locker room. After a sequence, you'll be right in the fray with your first Blitzball game!
Winning the Blitzball Match
Although theoretically possible without the Jecht Shot, winning your first real blitzball game without it would be extremely tough, especially considering the strength of your opponents. Even with the Jecht Shot you will find it hard to win without using the following tactics, although if you do lose don't be put off from blitzball as any subsequent matches are likely to be considerably easier.
The First Half
Your first action should be to hit and change to control from 'Auto' to 'Manual A', which will allow you to control your team rather than the CPU. In the first half you should refrain from attempting to attack the opposition's goal as soon as you get the ball, and instead pass the ball to Tidus. If you are unlucky , the other team may score before you get your hands on the ball, but you shouldn't be disheartened as you will automatically receive the ball after this, and it is still perfectly possible to win from 1-0 down (although you may consider resetting if you are 2-0 down at any point).
When Tidus receives the ball, taking care to watch the mini-map to ensure none of the opposition are too close to you (quickly pass if this becomes the case), swim back towards your goal so that you are about one quarter of the way up the pitch, and towards one of the corners. For the rest of the half pass the ball between Tidus and another member of the Aurochs (preferably one with a high pass attribute) by mashing as the ball is about to be received, and passing it straight back. So your first half of play should consist of stealing the ball, and then constantly passing it back and forth between the Tidus and one other Auroch until the time is up.
The Second Half
If you have done this correctly, at the half Tidus and the other Auroch will have gained enough exp. to gain some levels. This must get Tidus up to at least lvl. 3 as this gives him an ability slot, which you should equip with the Jecht Shot post-haste. The Jecht Shot not only adds 5 to your shot attribute when used (after selecting the shoot command after pressing or being tackled), it also knocks out 2 of the oppositions defenders out of the way (ignoring their tackle attribute).
In the second half again try to steal the ball and pass it to Tidus, but instead of retreating back to your goal move as close to the Goers' as you can without being tackled. If you think you are near enough the goal when you get tackled shoot using the Jecht Shot, as Tidus gets sent off early in the second half for Wakka, so you may only have the one chance. Bear in mind if confronted by 2 defenders the Jecht Shot will knock out 2 of them, so it is not worth trying to break through them. If confronted by 3 defenders however it may be worthwhile to break through one of them, then knock the other 2 out with the shot leaving just the keeper to contend with. Although Tidus' pass stat is terrible, his endurance is quite high.
Due to the time the Jecht shot takes, and the 120 HP cost, you will probably only get one chance to use it (although if you get a second chance make sure you take the opportunity) before Tidus gets replaced by Wakka. After this occurs if you are winning you can defend (run away if you get the ball, or continually pass it), or if you are feeling confident or you're behind/drawing you can try your chances with Wakka's Venom Shot, which has a good chance of scoring if you get close enough.
If you do manage to win this match you will receive a Strength Sphere for your efforts. This doesn't sound like much, but will add a +4 strength node to any empty space on the sphere grid. At this point in the game the best person to 'give' this to would be Auron as it will make his attacks do around 800 more damage, and best suits his attack style at this point in the game.
Escaping the Sphere Pool
Unfortunately, it's not over yet. For some reason there are fiends in the sphere pool! Tidus and Wakka are your only party members. One hit from Tidus will kill a Sahagin Chief, but it takes two from Wakka (using Cheer once or twice can change that). Keep fighting them until there aren't any left (more will swim into to replace the ones you kill) to progress across the sphere pool. After this, Auron will show you exactly what he's made of by killing the big bad dragon thing in one hit. You'll then have to fight a Garuda with Tidus and Wakka as well. Firstly cast Haste on Auron (he's slow) then use Dark Attack with Wakka. Auron should then use Power Break. The Garuda has 1,800 HP and will counter-attack often, which is why Dark Attack is so important. Other than that just physically attack the Garuda until it dies.
As if Auron showing up didn't lay down enough pain, Seymour will join in! You now get to watch fiends exploding in rainbow light, and you'll be prompted to save yet again (the game's being rather generous, isn't it?) and Wakka will leave the Aurochs to assist Yuna on her pilgrimage. If you won the blitzball match he'll hand over a rather large and impressive trophy to them, then walk off. Tidus will confront Auron, and one thing will lead to another. You'll also find out a shocking truth — which is not going to be said here. Follow the red blinking arrow all the way up to the balcony where you met Luzzu and Gatta before.
Afterwards you'll now get to press onward. You're headed for Djose Temple, but first, it's Mi'ihen Highroad.