The Archon's Forge is found in the Plaguelands and is similar to the Court of Oryx from the Taken King expansion. You will only be able to enter after completing the Rise of Iron questline, which will trigger Devil Splicer enemies in the Plaguelands to begin dropping SIVA Offerings. These items will be used to start an encounter, similar to the runes that were used to trigger Court encounters.
Here is a video showing you exactly how to get to the new public events in the archon's forge and how you start them! (must have SIVA offering to start!)