Due to the Azure Flute not being officially distributed, it is impossible to legitimately access the Hall of Origin.
When the player returns to the Spear Pillar with the Azure Flute, he or she will be asked to blow into it every time they step one tile north from the entrance until they catch Arceus. Upon doing so, a glowing staircase will appear, leading to an elevated glass platform high above the Spear Pillar, where Arceus awaits the player's challenge. While the player ascends the staircase, the camera will broadly tilt upward and zoom out, giving the player a unique view of the area below. Stepping onto the edge of the glass platform will automatically initiate the encounter sequence and battle. Should Arceus be defeated rather than caught, it will "disappear from sight" but the Azure Flute can be reused to summon it again.
In terms of game mechanics, when the player accesses the Hall of Origin by blowing the Azure Flute, they are actually no longer on the Spear Pillar but rather in a completely separate location, as evidenced by the screen fade-out transition and the change in location header. That is, the game does not place stair tiles onto the Spear Pillar map, but rather warps the player to a new map containing the stairs where the surrounding area looks identical to the Spear Pillar, exactly down to the cave opening that still leads into the mountain interior. This dispels a rumor that cheating to reach the Hall of Origin would trap the player on the elevated glass platform without the stairs to lead back down.
If the Sinjoh Ruins event has already been activated with an eventArceus, another Arceus caught in the Hall of Origin may be used to go back to the Sinjoh Ruins and choose one of the two Pokémon that were not chosen previously. The reverse order is also possible. There is no way to choose the third Pokémon.
Two versions of the Hall of Origin map exist in Pokémon Diamond, Pearl, and Platinum: one is the real location while the other is a "fake" copy. The "fake" Hall of Origin uses Spear Pillar as its theme and can be accessed through the void glitch using "Stickyman's Spear Pillar Hall of Origin" method, named after its discoverer. The "fake" Hall of Origin contains no warps or events and no Arceus. (YouTube video)
Unlike Darkrai and Shaymin, simply obtaining access to the (real) Hall of Origin (e.g. through the void glitch) does not mean that the player can battle Arceus there. This is because the scripts in the area are normally programmed to only trigger through the Azure Flute script in the Spear Pillar. The player can ascend the stairs, but the script to uniquely tilt and zoom the camera will not activate, nor will the script to have Arceus challenge the player when they step onto the glass platform. The Arceus sprite still appears, but just as in the actual event, it cannot be directly interacted with. Additionally in Pokémon Platinum, as with Darkrai and Shaymin, the Arceus sprite will not appear in the area at all unless the player has the Azure Flute in the Bag. To actually battle Arceus in the Hall of Origin, the challenge script itself must be triggered (see Pal Park Retire trick).