The right-hand stall is property of the guy who can never remember anything for long: the Move Deleter.  He will make your pokemon forget moves for free.  This is a useful way to blank off Hidden Moves from pokemon, who cannot replace them with other moves normally.  The Move Deleter can become absolutely vital to getting your team set up properly, particularly if you add members to whom you want to shift the burden of Hidden Moves, or if you reach a point where you no longer need to have the Hidden Moves on the pokemon that you are using to battle with (usually after scouring the whole map for hidden items).

Continue East from the stalls and you'll find Clay and Hugh waiting for you again, this time outside a large building at a crossroads.  Clay greets you and then indicates the huge building with its display screen over the entrance.  This is the home of the Pokemon World Tournament, and Clay immediately enters and ushers you in.  You and Hugh follow the Gym Leader inside, where he tells you he's having you participate in the Driftveil Tournament.  This is a single-elimination tournament with eight participants- anything goes, and winning three times gives you a championship.

This is when Cheren, who's been waiting beside Clay, interrupts to find out why he's been brought here.  The local turns to the younger Gym Leader and explains that, as Cheren is the one who has to show everyone what pokemon battling is really about, he's got to represent himself as a worthwhile battler.

The studious Gym Leader is a bit exasperated, but can't help being at least a little enthusiastic about the tournament.  He and Hugh head up to the receptionists to the North to register, with your old friend prompting you to join in as well, to have a 'good simple battle'.

To either side of Clay, you can find the Battle Exchange clerks, who will convert the BP you win here and at the Battle Subway into items of your choice.  Before you head into the tournament, step back outside- there's a bit more going on here.  Immediately to the East is a stall where the starters (Charizard, Blastoise, Venusaur, Typhlosion, Feraligatr, Meganium, Blaziken, Swampert, Sceptile, Infernape, Empoleon, Torterra, Emboar, Samurott, and Serperior) can learn the Fire/Grass/Water equivalents of Hyper Beam.  These moves are powerful, but make no mistake- they are costly to use.  At minimal PP, with an accuracy of 90 and a recharge turn after every successful hit, you have to pay and pay hard for that 140 base power.  That said, anything hit with them is virtually certain to be unconscious afterwards.  Choose carefully when deciding to get these moves or not.