1 Get an old key
If you are using Chris, you will need an old key to unlock the room with the broken shotgun. Jill, on the other hand, will just use her lock-pick to unlock the door. The old key can be found in many areas of the game.
2 Get the broken shotgun
The broken shotgun is found in the west wing of the mansion's first floor. Go to the corridor which leads to the typewriter room in the west wing (the small room). In that corridor, one of the doors leads to a very small room which has the broken shotgun.
3 Go to the shotgun room
The shotgun room is in the east side of the first floor. Reach the eastern room with the Typewriter. From there pass through the first corridor to the second. The second corridor has a small room that leads to the shotgun room.
4 Grab the shotgun
Grab the shotgun from the wall. Note that this activates a trap that will kill you if you try to get out.
5 Replace the broken shotgun
The main purpose of the broken shotgun is to replace the original shotgun so that you don't activate the death trap.
6 Leave the room normally
Once the broken shotgun is in place, the trap won't be activated and you will be able to leave the room normally.
7 Jill doesn't need the broken shotgun
If you are playing as Jill, you won't need the broken shotgun, for Barry will come to your rescue once the trap is activated. Only Chris needs that broken shotgun. Note that you can still do the same with Jill and escape Barry's help.