To begin History of Magic Class, you need to go into the classroom and attend the class. Take the Bell Tower Courtyard Floo Flame and go up the stairs south, then through the door in front of you. Then, just ahead, you will find the classroom. Walk partway into the room and press / to begin the quest.
During the class, your character will start struggling to stay awake. When this happens, quickly move left and right until you’re fully awake again. After the cutscene, Professor Binns will walk out of the class — follow him and the rest of the class until you reach the Bell Tower Courtyard. Once you reach it, you will start a conversation with him, and he will ask you to find two Field Guides Pages.
For the rest of this quest, you cannot leave the Bell Tower Courtyard, or you will abandon the quest.
Find the Grimbald Welf Field Guide Page
The Field Guide Page about Grimbald Welf will be just south of the Floo Flame — you will see a display featuring a skull. To reveal the page, you’ll have to cast Revelio while standing right in front of it. Once it’s revealed, grab it and you will get into a conversation with Professor Binns. After you’re done speaking with him, you will have to find the next page.
Find the Sir Affpuddle Field Guide Page
To find this Field Guide Page, go up the stairs on the north side of the room, then up the stairs just to the right of them. The page will be all the way on the left, in front of the knight that will wave hello to you. Cast Revelio while standing in front of it, and you can collect the Field Guide Page.
Speak to Professor Binns
Once you have the Field Guide Page, return to Professor Binns, who will now be in the center of the Bell Tower Courtyard. Speak to him to learn a little more about Sir Affpuddle.
After speaking with him, you will have completed History of Magic and have a new Conjuration for your Room of Requirement!