Head down the steps to your north. Now follow the path west until you come upon two sets of stairs. As you may as well make the most of teaming up with Hugh, it's better to take the south set of stairs first and explore all that you can before heading up the north set. Therfore, move up the southern set.
Once you reach the top, you'll see a person to your west who will stop you from moving past him until you defeat the Team Plasma Grunts in the Sewers. Don't worry about him just yet and head south instead. When you see a thin set of stairs leading down to the area below, move down them.
Head south until you reach the stairs leading up west. Move up them and grab the X Sp. Def from the platform above. Move back down the stairs and head south, then west. Keep going until you reach the point where there is a path leading north and another south.
The south one's a dead end, so head north, moving up the stairs when you come upon them. Near the top of the stairs you'll find a Worker.
Trainer Battle: Worker
Once he's defeated, head north past him, down the stairs taking you west and back up the next set. Here you'll find a Doctor! Talk to him if you want a fight.
Trainer Battle: Doctor
From now on, anytime that you talk to the Doctor that you just defeated, he will heal your Pokemon . As your Pokemon already automatically heal between battles because you're travelling with Hugh, there's little need for this though. Move right, past the door.
You'll notice another item on the ground. Go over and pick it up. It's some Leftovers . Now enter the door that you just moved past. Inside, a scientist will give you a random healing item from a small range of possible ones. You can return here once per day to receive another. Once you're received it, leave the room.
Backtrack past the Worker and head down the steps near him. Now continue on north, then east. You'll reach some stairs. Move up them and take on the nearby Scientist.
Trainer Battle: Scientist
There's nothing in the room next to her, so head back down the steps, then head west, south, east and finally north until you reach the steps that you first came down. Continue south along the path here until you reach the Janitor. Battle time!
Trainer Battle: Janitor
Head past him and move down the steps at the end. Follow west along the path until you reach the very end. Move up the stairs here and take on the worker.
Trainer Battle: Worker
Afterwards, grab the Pearl obscured in the alcove to the Worker's east. Now backtrack all the way back past the Janitor back to where you had to choose between the two sets of stairs near the start of the area. This time, move up the northern set. Head west until you reach the TwistedSpoon , which you should pick up.
Move toward the Plasma Grunts to your north. After speaking with them you'll enter into a Double Battle.
Double Battle: Team Plasma Grunt & Team Plasma Grunt
The Grunts will scram after you defeat them... and Burgh, the Gym Leader will appear! After talking, Hugh will give you HM04, which teaches Strength . He will soon leave. A strange man will then appear from the door to your north and promptly leave. It's your first interaction with Colress!
Finally, Burgh lets you know that he's now back in his Gym and also leaves. It's now back to single battles again. If you enter the door to your north, you will enter an entirely separate area known as Relic Passage .
This is only part of the Relic Passage though. It isn't too big and has a few trainers and a few nice wild Pokemon, so you might consider exploring it. If you wish to explore it, do so, otherwise exit the sewers at the same place that you entered it.