From Castelia's Pokemon Centre, continue left and enter the building just to the left of the next street. This is the Battle Company building. Inside, you'll find a number of trainers itching for battle, so it's a good place to train. Not to mention there are some decent item rewards, so it's definitely worth a look.
As soon as you move forward in the 1st floor you'll be stopped by a person who'll give you an Exp. Share before taking the elevator to one of the upper floors. Talk to the blue-haired girl sitting at a table to your right. She will give you an item depending on which dialogue option that you choose.
|Miracle Seed, Mystic Water, Charcoal|
If you pick the last option, you can come back later and still claim an item. Choose whichever item suits you best. You can actually obtain all three items for free within Castelia's general vicinity, so no need to stress your decision too much. Once you have your fancy new item, enter the elevator and go to the 47th floor first.
The 47th floor features a decent array of trainers. If you simply want to skip the trainers and collect the only item reward that you can without fighting, sneak past the trainer to the right of the room by staying as far left as possibly without moving into sight of the man in the top-left corner.
From there, simply move past the man in the centre of the room on his left side, then move around and speak to the person in the bottom-right corner who will award you with a Scope Lens . Move back to the elevator the same way.
If you do plan to battle the trainers though, the information is found below.
Trainer Battle: Clerk Male (Top-Left Corner)
Note: The man rewards you with two Quick Balls for defeating him.
Trainer Battle: Clerk Male (Center-Right of Room)
Trainer Battle: Clerk Male (Center of the Room)
Note: The man rewards you with five Timer Balls for defeating him.
Trainer Battle: Clerk Female (Bottom-Left Corner)
Once all trainers have been defeated, don't forget to talk to the man in the bottom-right corner of the room to receive the Scope Lens , then leave the floor.
You may want to go back to the Pokemon Center and heal your Pokemon first. Once you have, come back and take the elevator up to the 55th floor. There's an Ether on the ground in the top-left corner of this room. Grab it then move to the top-right area of the room.
You'll be stopped once again by the man that gave you the Exp. Share earlier. He'll reveal himself as the grandfather of the CEO of the company, who happens to be a School Kid. As soon as you're stopped by the man, you'll be forced to battle the School Kid, so make sure you're ready beforehand.
Trainer Battle: School Kid
After you've taught the kid a lesson, you're done with the Battle Company. Return to the elevator and let it take you back to the 1st floor and then exit the building like a pro.