The Adamantine Forge is located in the Underdark during Act 1. Work your way to the Underdark Beach and take the Underdark Duergar Boat to Grymforge. In the northeast corner, you will find a few Duergar heardmasters with 2 Deep Rothes trying to clear rubble to the forge. Either agree to help them, or convince the animals to attack and help free them. After that, get the animals to clear the rubble and follow the path.
Scattered around the area are weapon and armor moulds and Adamantine Ore. When you reach the forge, insert the mould you want to use in the Mould Chamber and place the Adamantine Ore in the Crucible. Then, pull the Forge Lever to lower the platform.
Ungroup and position your party on the circles since the rest of the area will flood with lava. Next, interact with the Lava Valve to start the flow. The first time you forge an item, you will need to fight Grym. Make sure you reopen the lava valve anytime it closes the valve. The lava needs to flow in order to damage Grym.
Once the battle is over pull the Forge Lever again to complete the process and walk over to the Mould Chamber and collect the gear. Make sure you pull the Mould Ejection Lever and collect the mould before leaving the area. When you’re finish, interact with the Platform Control button near the Forge Lever to return the platform to the top.
If you choose to forge another item, the forge will get stuck with the lava on the platform. To fix it, change to turn-based mode and end your turn a few times.