Each Forge in the Black Armory comes with different frame unlocks, so you're going to need to know how to unlock the Izanami Forge in Destiny 2. Be warned, this is easily the longest Forge quest in the game, and you'll have to do it on all your characters if you want full Forge access. So, we've rounded up all the quest steps and thrown in some tips to help speed up the process.
Start the Izanami Forge quest by killing Vex. You can do this anywhere, but you should kill them on Nessus, as that's where the quest will lead you. Once you get a Vex Transponder drop, kill 100 more Vex on Nessus to juice it up. Public events and Lost Sectors are great spots for finding groups of Vex. You'll also need to clear the Heroic Spire Integration Public Event for the next step, so it's worth tracking it down.
After 100 kills and the Heroic Spire, you'll need to kill 20 Vex Minotaurs in Artifact's Edge, the Glade of Echoes, the Hallows, or Watcher's Grave on Nessus. The Heroic Spire is a great source of Minotaurs, as it happens, but they'll also spawn pretty much everywhere. A few dead Minotaurs later, you'll get a mission that leads you to the Izanami Forge, but we're not done yet.
Clear the mission and talk to Ada-1 to receive the Izanami Forge Igniter. You need to fix the Igniter to unlock the Forge, and that's no easy task. First, complete three more Heroic Public Events: Glimmer Extraction, Spire Integration, and Witch's Ritual. These can be found on multiple planets, but the best locations are the EDZ, Nessus, and Titan respectively. The Witch's Ritual is a rare event, so keep checking Titan on your Destinations map while you're doing other events to see if it appears.
To complete this solar system-hopping quest, you need to destroy Taken Blights in Lost Sectors on Io - the one near the starting spawn works best - and complete another mission on Nessus. Oh, and you need to get Fallen precision multikills, which you can easily do in the EDZ. Once all that's done, head to the Gofannon Forge in the EDZ to charge up the Igniter for real this time. But we're not done yet: now it's time for a buffed version of the Insight Terminus Strike on Nessus. I told you this was a long quest.
Finally - finally - you can complete the actual Izanami Forge mission, talk to Ada-1, and claim your weapon frame. I'll bet you can't wait to do that again on another character, eh?