Vault 75 (quest)

Vault 75 is a side quest in Fallout 4 which is triggered when exploring Malden Middle School.

Detailed walkthrough
In the basement of the Malden Middle School, go through the Vault door and enter the elevator going down. After exiting, turn right, then keep going in that direction until encountering a door to the lab on the right-hand side marked SECURITY that needs an access card to be opened.

At the end of the hallway, one will get to the atrium. Go forward and turn right into a locker room to see another hallway at its end and inaccessible door to the lab from the other side. Go left, down the stairs and left towards a diner. Go into it and upstairs and get the access card from the tool case.

Head back to the second blue door and open it with the access card. The door in front of the player character leads to the first blue door, it is just around the corner to the left.

Go up the stairs and one will find yourself in a room going three different ways; go forward. Kill the Gunners and get the admin access card from one of them. Now the player character should be in a room with a view to the diner they have been to previously. A Science bobblehead is on one of the tables.

Backtrack to the lab room and use the admin access card on the door marked OVERSEER. Climb up a few stairs and one will be in the overseer's room. Activate the terminal on the desk to complete the quest.

Upon entering the overseer's room, on the right is their bedroom with a Grognak comic on the bed.

Bugs

 * Even after completing the quest, one may not be able to remove the Vault 75 access cards from their inventory, as they will still be flagged as active quest items.
 * Even after completing the quest, the entrance door to Vault 75 may still say "Malden Middle School Basement," even though Malden Middle School has been renamed to Vault 75.
 * Modded saves have a very high chance of tripping a bug that causes the access cards needed to progress to not appear in the inventory of the NPCs or containers they should. The quest can be finished as normal by adding the cards to the player via console commands or by any mod that provides an alternate means of acquiring them in the game world.