Legendary Crafting in Shadowlands is unlocked after completing the Torghast Campaign Chapter and cultivating 1250 Soul Ash.
Once you reach level 60, complete the campaign, and choose a Pact, you initiate the next stage of the Shadowlands campaign. The first chapter is basically a tutorial for your Covenant and the endgame systems in Shadowlands, and the biggest obstacle to your campaign progress will be the quest to farm 1000 Anima. While this will become a weekly task that will increase your fame, it is mandatory at this point if you want to deepen the campaign to unlock Legendary Crafting.
Once you've dropped 1000 Anima into your Covenant's tank, you'll move on to the Soulbinds tutorial and then be taken to Oribos. Bolvar and his company will task you with returning to the Maw, which will launch Chapter 2 of the campaign. This chapter may be called "Torghast", but it is also a tutorial for the Maw itself. You'll meet Ve'nari, and she'll ask you to complete a handful of quests that introduce you to your second weekly Fame Quest and basic Maw functionality. Don't go mad just yet and maximize your Eye of the Jailer, otherwise you'll have to come back another day to completely complete some subsequent campaign quests for Legendary Crafting.
Once you've knocked them out, she'll direct you to Torghast. You'll have a quest inside, and you'll need to complete at least one layer in one of the available rooms to advance the campaign. You should come across a key to the Runecarver chamber which is immediately to the right of the Torghast entrance, and you'll have a quest to venture inside.
Once inside, talk to the Runecarver. You will have to kill an enemy in the Maw to recover some of its memories, then you will be responsible for cultivating 5 embers of the “elementals” of fire in the Cauldron. That's why you'll want to keep your Jailer's Eye low: Maximize it during the first few quests and you won't be able to complete either of these two quests until the next day. After you return to Ve'nari with the embers, you can purchase a quest item from him. Return to the Runecarver and "free" it from at least one of its chains. It will then provide you with two quests, although one is not required to unlock the Legendary Crafting itself (it provides your Legendary Crafting component recipes if you are an artisan).
You will then be tasked with cultivating 1250 Soul Ash from Torghast ("Ashes of the Tower"), and completing this quest will unlock Legendary Crafting in Shadowlands. Until the second set of layers becomes available on December 8, it will take you two weeks. Currently, you can only erase the first three layers of the two available chambers, which means you will cap at 810 Soul Ash for the week. You can technically farm Soul Ash in small amounts from the Adventure table, but only from high-level missions that you won't be able to access for a period of time. THAT IS TO SAY. Clear all 6 layers available if you want to unlock Legendary Crafting within two weeks of starting Shadowlands.
Once you return to the Runecarver with the Soul Ash, you will unlock the Legendary Crafting. You will need a basic legendary component created by a crafting profession (like the neck and ring made by jewelers), you will have learned a legendary power (these drop all over the Shadowlands, although clean up layer 3 of each chamber seems like a solid way to earn two from the start), and possess the required amount of Soul Ash for the runecarver to create your Legendary.
That's right: you'll need to farm Torghast if you plan on crafting Legendaries. Simply interact with the Runecarver to bring up the crafting interface once you've got everything and craft the Legendary you farmed Soul Ash for. If you're not a craftsman, expect to pay a lot of money over time for legendary components. I recommend leveling up a crafting class if you haven't saved gold already.