Meet Professor Weasley in the Transfiguration Classroom
First things first, you’ve got to make your way to Professor Weasley. You can use a nearby Floo Flame if you want — the Transfiguration classroom is by the Astronomy Wing, and then you can use the Transfiguration Courtyard or Classroom flames if you’ve unlocked either of them. Head to the spot indicated by the objective icon (don’t forget you can hit up on the d-pad if you’re lost) and then stand in the golden circle. You’ll then be able to hit /to begin the Quest.
A cutscene will play, in which you’ll be told more about your extra assignments. Class Assignments are a specific type of side mission — unlike some of the other side mission categories, these are generally required to progress in the main story, since they allow you to learn spells that are necessary for completing some of the main story quests. This doesn’t mean you have to do them right when you get them — but it’s usually a good idea, since you don’t want to go try and do a quest only to discover you can’t complete it!
At the end of your conversation with Professor Weasley, she’ll tell you to go to Hogsmeade to pick up a wand from Ollivander’s. You can choose Natsai Onai or Sebastian Sallow to join you on your trip to town — you’ve met both of them already, so pick whoever you’d rather spend a long walk to town with, and you’ll have completed this quest!
It’s best to report to Professor Ronen for your first Class Assignment now, as doing so will allow you to learn the crucial Reparo spell.