When you enter the vault you must jump over the railing into the first big room, then go through the door dirctly in front of you and take the stairs down. Make a left and continue to follow that corridor until you see a left turn where water is pouring from the roof, go down into the flooded area to the room at the end and look left. You will find a dead glowing one under a desk, he has a password you need. Come back out of the flooded area and turn left then right, make another left and go through the first door on the right (the old medical bay). Go through the room and keep following the corridor until it turns left. Take the door that is directly in front of you and go down this flooded area, you will find another dead ghoul at the end of the room, grab the password from him as well and go back up. Afterwards turn to the left and go into the room with the open door. You need to input the password into the terminal there and open the "system" directory. After, go back through the medical bay and to the overseer's office (turn left and go around the corner with the green goo on the floor). Go down the stairs and turn left. Activate the terminal at the back of the room and select "system" and "open armory door". Go back up the stairs and out of the room and through the medical bay again. Then make a right then a left and keep going to the door at the end (listed as armory). After going down the stairs turn right and go into the first door on the right. The armory is right there.