Beating Clay has earned you a special honor: You're one of the first people to participate in the all-new Pokémon World Tournament! Most excellent. This is another area where you can earn Battle Points and exchange them for fabulous prizes. It's not as fast as the Battle Subway right off, but you get the chance to battle some trainers you might not normally see in Unova - including a ton of gym leaders from other regions.

When you show up with Clay and Hugh, you'll find Cheren waiting. Clay encourages all three of you to enter, and Hugh and Cheren will rush in to participate in a tournament. You can join them, but first have a look around the entrance area. There's a lot to see:
  • To the southwest of the entrance is a path to Relic Passage. You were able to visit this place earlier, from the Castelia Sewers, but now's a much smarter time to do so. More on Relic Passage after the events of the Pokémon World Tournament.
  • The girl in the booth east of the Relic Passage is a Move Relearner. She'll re-teach your Pokémon any moves they might have learned during their lifetime in exchange for a Heart Scale. Very handy, as some moves probably weren't available to your Pokémon when you first got it.
  • To the left of the Move Relearner, hidden on the ground, is an Ether. Pull out your Dowsing Machine to find it.
  • Next to her is the Move Deleter. He'll permanently remove any moves from your Pokemon's arsenal. This is the only way to remove HM moves like Fly, Surf, and Strength from your Pokémon.
  • North of the Move Deleter is a man who will reveal the nature of your Pokemon's Hidden Power move. Each Pokémon receives a different move type when using Hidden Power, and this man will tell you what it is without the need for experimentation.
  • Down on the dock you'll find a PP Up.
  • To the right of the main building is a man who will teach an 'ultimate move' to the final evolution of any of the starters from the various Pokémon games. Note that you must have the final evolution to learn these moves.
  • Next to this man is another Move Tutor who will teach your starter Pokémon one of three 'Pledge' moves, depending on its type. Pledge moves are made more powerful when used in tandem, so they're only really effective in team battles - and even then, you can only give them to starter Pokémon.
  • In the far east, next to the fountain, you'll find a worker who will give you a Rocky Helmet.
  • In a trash can beside the vending machines to the north of the Move Tutor is a Zinc.
Enter the main building. The only notable thing here at the moment is the Exchange Service desk, where you can trade in BP for prizes. There will eventually be special tournaments, as well, available via the check-in woman in red. For now, talk to the woman in green to begin the tournament. 
You can only use three Pokémon in each battle, so choose your wisely - your first battle is against Hugh, and he's never a pushover.

Pokémon Trainer Hugh
  • Pignite, level 25 (if you picked Snivy), Dewott, level 25 (if you picked Tepig), Servine, level 25 (if you picked Oshawott)
  • Simipour, level 25 (if you picked Snivy), Simisage, level 25 (if you picked Tepig), Simisear, level 25 (if you picked Oshawott)
  • Tranquill, level 25
So long as you don't play to Hugh's strengths and keep deploying either neutral or super effective Pokémon, you should win easily. Beat Hugh and you'll advance to the semi-finals, where you'll face Cheren.

Pokémon Trainer Cheren
  • Stoutland, level 25
  • Cinccino, level 25
  • Watchog, level 25
If you have even a single Fighting-type Pokémon, Cheren is a piece of cake. Even without he's not that hard, as your Pokémon will probably be around level 30 by now.

Pokémon Trainer Colress
  • Magneton, level 25
  • Elgyem, level 25
  • Klink, level 25
Colress remains more of a nuisance than a huge threat, given that two of his Pokémon are Steel-type and rely on their defenses to survive. Fire- or Fighting-types should have no trouble here, though watch out for Elgyem zapping your Fighting-types with its Psychic-type moves.

Winning the tournament will net you a cool 1 BP. Hardly overwhelming, but enough to buy you an expensive Vitamin, if you wish to use it now. You'll also get a surprise visit from Roxie, hinting that you'll wind up challenging all of the Unova gym leaders again if you keep coming here. What fun. Continue to participate as long as you wish, but be ready for trouble when you leave -

- because a Grunt from Team Plasma will rush past. Apparently the diversions of the day are over. Back to the story.