In order to return to the Northern Undead Asylum, you must first have activated the short-cut elevator that goes down to the Firelink Shrine from the Undead Parish. Before you return to the Northern Undead Asylum, it is advisable to get the Undead Asylum F2 East Key from the roof of the building where Petrus of Thorolund is located. Getting this key ensures that you can collect everything possible from the return to the Northern Undead Asylum in one trip. It is also advisable to return to the Northern Undead Asylum as soon as possible in order to get the Rusted Iron Ring.
Get on the elevator from Firelink Shrine and, as the elevator starts moving up, you must move forward and drop on top of the area where you enter / exit the elevator at the bottom. Follow the path to the right, on top of a little green patch of grass, then look down and you will see a broken column. Roll towards that broken column and land on it, then go up the beam. This will take you to a set of stairs. Go up the stairs and when the stairs make a 180 degree turn, you will see a roof directly in front of you. You should also see a corpse on the roof clutching an item. Jump onto the roof and collect the UNDEAD ASYLUM F2 WEST KEY. Make your way back to the elevator, jump onto the roof of the elevator entrance, head across the grass patch, jump onto the beam and head up the beam to the stairs. From there, climb up the stairs all the way to the top where you will find a crow's nest (similar to the one at the Northern Undead Asylum). Step in to it and you will get a prompt to Curl Into a Ball. If you curl up into a ball and wait about 30 seconds the crow will pick you up and bring you back to the Northern Undead Asylum, dropping you off in its nest there.
Upon returning to the area the first thing you will notice is that the Zombies are wielding torches. Since the player typically has horrendous fire resistance, these foes deal heavy damage to you if they can connect. Be cautious when engaging these enemies, as they can easily wreck you if you are not careful. The only new area unlocked in the Northern Undead Asylum is the third level's west wing (where you may have noticed an item which you could not collect after the very first fog gate of the game). If you recall from your first run-through of the area, the door behind the lone Undead Soldier (Sword) on the third level's west wing was locked, but is unlocked with the Undead Asylum F2 West Key which you should have just gotten from the Firelink Shrine on your way back to the Northern Undead Asylum.
Before you start wandering around aimlessly after entering the building, ensure that you don't walk anywhere in the center of the room (marked by the part of the floor which is lowered by two steps) where you fought the Asylum Demon because the floor will collapse and you will prematurely fight a tough boss in the pit, the Stray Demon.
If you head back to the second level where the Elite Knight died, you will notice that the boulder trap will have reset. Activate the trap a second time to re-open the hole in the wall, and the Elite Knight will emerge, now hollowed and hostile. He is a tough opponent, but has a slow roll and will be vulnerable after each roll and when he is wielding his weapon with both hands. Play defensive and attack only when you have the opportunity to. Being too aggressive could lead to your early demise because he has a good damage output. End his suffering and he will drop his CREST SHIELD, a very powerful magical shield with one of the highest magic deflection rating in the game.
Third Floor, West Wing
On the third level's west wing, you can unlock the locked door in the western room with the Undead Soldier (Sword). This room now also has an Undead Soldier (Spear), making a total of two Undead Soldiers to deal with. Behind the locked door (which you unlock with the Undead Asylum F2 West Key that you find in the Firelink Shrine) you will find the RUSTED IRON RING, which is a very useful ring for certain parts of the game.
Two Black Knights will be present during your return to the area, who will not respawn when you kill them. One will be in front of the cell which you started the game in, and he will be guarding the PECULIAR DOLL which is now mysteriously sitting in your cell. The other Black Knight is at the end of the hallway where you got your starting class' weapon and shield, in place of the Zombie archer.
Boss Room Revisited
Whenever you are ready, head to the center of the room where you fought the Asylum Demon. The floor will collapse and you will fall into the pit which you can see from the hallway leading to and from the cell you start the game in. Here you will fight the Stray Demon, a tougher version of the Asylum Demon.
Boss Fight: Stray Demon
Defeating the Stray Demon will grant you 20,000 Souls, a TITANITE SLAB, a consumable HUMANITY ITEM, and a HOMEWARD BONE. After you have collected the few new items in the area, you can continue with your journey back on the mainland of Lordran.