Part 1: Crystal Farm or Convert Zeta
If you do not have a Zeta Zodiac then you will need 3 crystals farmed from FATES in each of the following zones: Sea of Clouds, Azys Lla, Churning Mists, Coerthas Western Highlands, Dravanian forelands, Dravanian hinterlands
Part 2: Dungeon Farm
After completing step one you will be asked to do the following dungeons in this order. Names in italics can be done unsynched at this time
Snowcloak, Sastasha (Hard), Qarn (Hard), Keeper of the Lake, Wanderer's Palace (Hard), Amdapor Keep (Hard), Dusk Vigil, Sohm Al, The Aery, The Vault
Part 3: 80 Unidentifiable Items and 16 Specialist Crafted Items
You will need to farm up a lot for this step, you`ll need 20 of EACH of the following: Unidentifiable Bone Unidentifiable Shell Unidentifiable Ore Unidentifiable Seeds
Easiest method I found for this was to do roulettes and beast tribe quests. For beast tribes try to stick to the ARR tribes (Need Rank 3+) as you only need to do 13 quests to get 1 item as opposed to 18 for 1 from the HW Tribes.
When you have the items you need you will also need 4 of EACH of the following
Adamantite Francesca, Titanium Alloy Mirror, Dispelling Arrow, Kingcake (CUL)
Each of these can be crafted by a specialist or purchased on the Market Board, as well as purchased with Company Seals.
Once you are done that part you will be trading the items in to an NPC in Mor Dhona and then taking the items to Azys Lla
More will be released down the road, I will most likely just update this thread as it comes out

Part 4 (Introduced in 3.25) Aether Oil
This part is fairly easy, you need to get 5 Aether Oils and at this time there are two ways to get them. One is with the weekly Crystal Tower quest "The Gift of the Arch Magus" which gives one oil. The other method is farming up 1800 tomes and buy an oil in Idylshire.

Part 5 Sands and Umbrite
This part is again easy, just time consuming as you will need 9000-12000 tomes. You basically get an umbrite from one of Rowena's girls in Idylshire along with a few items for the NPC Ardashir (Has a diamond carbuncle beside them). Trade the items for crystal sand then augment the weapon to convert the sand + umbrite into the required material. The easiest I found was using Thavnarian Mist x 5 with Superior Enchanted Ink x 5 for the sands.
Part 6: Singing Clusters x 50
You can buy these with tomes and also do some repeatable quests to get all 50
Part 7: Do the 3 dungeons they list, easy enough, then do HW dungeons etc to gather density (Light Farming 2.0)
Part 8: Get 15 pneumite, just use tomes or seals
Part 9: Do all the listed trials, there will be 12, you'll need an Archaic Enchanted ink at the end of it, then you are done