I think your excerpt might not contain the correct text. My copy of the book has the sentence worded a bit differently:
Classroom eleven was situated in the ground-floor
corridor leading off the entrance hall on the opposite
side to the Great Hall.
This makes it somewhat easier to understand. The classroom is in a corridor. The corridor is on the ground floor ("ground-floor corridor"). The corridor leads off the entrance hall. The corridor is on one side of the entrance hall and the Great hall is on the other side of the entrance hall (opposite side to the Great Hall).
To understand this better, we can picture the entrance hall as a central room that leads to other areas all around it. If we go back to the first book we can see some descriptions that help here:
She pulled the door wide. The entrance hall was so big you could have fit the whole of the Dursleys' house in it. The stone walls were lit with flaming torches like the ones at Gringotts, the ceiling was too high to make out, and a magnificent marble staircase facing them led to the upper floors.
They followed Professor McGonagall across the flagged stone floor. Harry could hear the drone of hundreds of voices from a doorway to the right – the rest of the school must already be here – but Professor McGonagall showed the first years into a small, empty chamber off the hall. They crowded in, standing rather closer together than they would usually have done, peering about nervously.
This passage tells us that the entrance hall has a staircase leading out of it, a Great Hall on the right (where the hundreds of voices are coming from) and another empty chamber. The empty chamber later seems to be opposite the Great Hall (i.e. on the other side of the entrance hall):
Feeling oddly as though his legs had turned to lead, Harry got into line behind a boy with sandy hair, with Ron behind him, and they walked out of the chamber, back across the hall, and through a pair of double doors into the Great Hall.
In the fourth book, there is a description of yet other areas branching off from the entrance hall, when they go find the kitchen:
She turned left at the bottom of the staircase and hurried toward the door through which Cedric Diggory had gone the night after the Goblet of Fire had regurgitated his and Harry's names. Harry had never been through here before. He and Ron followed Hermione down a flight of stone steps, but instead of ending up in a gloomy underground passage like the one that led to Snape's dungeon, they found themselves in a broad stone corridor, brightly lit with torches, and decorated with cheerful paintings that were mainly of food.
Thus, the corridor that leads to the Kitchen also starts from the entrance hall, and apparently on the same side as the Great Hall.
So getting back to the original excerpt, it seems to simply mean that the corridor branched off from the entrance hall, and it was on the other side of the entrance hall and not the side where the Great Hall was. Here is an illustration to help (not drawn to scale, and not perfectly accurate):
Here you can see how he corridor with classroom eleven is opposite the Great Hall – it is on the other side of the entrance hall.
From some of the other comments, it seems like the confusing part might be the phrase "opposite side to". This can be replaced with "opposite side of" if that helps you understand it better.
Note that in your version of the excerpt it is possible (grammatically) to understand it in an entirely different manner. The phrase the corridor leading off the Entrance Hall from the opposite side to the Great Hall could be taken as describing the location of the corridor as extending from the opposite side to the Great Hall. I.e. "the opposite side" is one location and "the Great Hall" is another location and the corridor goes from one location to the other location. In this reading the word "to" would not be part of the phrase "the opposite side". However, this reading is untenable from what we know from other descriptions (e.g. that the Great Hall is described as being right off the entrance hall and not down a corridor).