Transmuting and reconstructing gear is a system in ESO that lets you change the trait or reconstruct gear you have once found but deconstructed in the game. This will not work for crafted gear by the way. But let’s back up a bit.
The Sticker book
The sticker book is a system in the game where all non crafted sets (trial, dungeon, overland, pvp, etc) are added once they are bound to your account. To bind a piece of gear you can either deconstruct it, destroy it or bind it via the context menu. Trial and Dungeon gear auto binds after 2 hours if you haven’t traded it away. Once an item is in your sticker book you can reconstruct it at a transmute station at a later point for Transmute crystals. The nice part is that once an item is bound it will not drop for you again until you have everything from the loot table from the boss you kill. (In trials and dungeons all bosses but the last boss will drop certain body pieces and only the last boss drops weapons and jewelry)
Side note: All items are added in the lowest drop quality to the sticker book no matter in which quality they dropped for you. For dungeon and trial gear this will be blue for overland gear green
Transmute cost
The more pieces of a certain set you have in your sticker book the lower the cost of reconstructing for it will be. The lowest Reconstruction cost you cab get is 25 which is nice since when you later figure out you don’t need the piece you can deconstruct it for 25 transmutes again (all upgrade materials will be lost tho).
Where to find a Transmute Station?
There is only one publicly available transmute station in the game.
It is in clockwork city inside the Brass fortress.
But fear not if you don’t have that DLC or ESO+ you can still use the Transmutation system. You can find Transmute stations in a lot of player houses or even get one for your self. You can buy them for Writ Vouchers or at guild traders for gold. Your easiest option would be to find someone who has one in their house (a lot of high level players do) and just use theirs. If you are in a guild there will probably be one in your guild hall. Otherwise you can use the home tours feature to find a house with a transmute station.
Transmuting gear
If your reconstruction cost is higher than 50 it can make sense to change the trait of a piece of gear you have instead of reconstructing it. Changing the trait always costs 50 transmute crystals no matter how high your reconstruction cost is. Important is that you have the trait researched for that certain slot. So if i want to reconstruct a Heavy chest plate in reinforced I will need to have the reinforced trait researched for heavy chests and so on. The same is true for reconstructing.
Reconstructing gear
Reconstructing is the most used method to make a piece of gear in the correct trade since you can just farm wherever the gear is coming from (or buy overland/pvp gear from guild traders) to fill up your sticker book to get the cost below 50 Crystals. You still need to have the trait researched for the piece you want to reconstruct. Then you just select the set from the menu at the transmute station and spent your transmute crystals for reconstructing it with the correct trait. There is no need to have the piece of gear in your inventory. You can reconstruct any piece of gear you found in the game at any point at your current level.