This quest is acquired near the beginning of chapter 2. Harrim will approach you in the throne room of your capital, informing you of some ancient dwarven ruins in the area which he would like to visit. The location of these ruins will become known to you after meeting Ekundayo during Troll Trouble - A Score to Settle.
Once you’ve learned the location of the dwarven ruins, make sure that Harrim is in your party before you venture to them. If you haven’t explored the region yet, take the following directions from the Ruined Watchtower:
When you enter the Dwarven Ruins, you should notice an update to the main quest Troll Trouble. You’ll find a detailed guide for the area as a whole at Troll Trouble - Dwarven Ruins.
With Harrim in your party, head up the path until you encounter a group of hostile Kobold warriors. These can be dealt with easily by any party at this level, and so shouldn’t cause any problems. Once the Kobolds are dead, proceed further west and then north. Here you’ll encounter two Trollhounds and a regular Troll. As with the Kobolds, they’re no match for your party.
With these intial enemies defeated, you should find yourself at the entrance to the dwarven ruins to the east. These ruins also happen to be the troll lair you’ve been searching for. In the courtyard, you’ll find a combination of enemies that you’ve already encountered, but you’ll also encounter some Branded Trolls and Greater Trollhounds. These are slightly tougher than their lesser counterparts, but good use of acid weapons, spells and scrolls will make short work of them.
Note: Be sure to rest up fully before you enter the Dwarven Ruins / Troll Lair. The fight ahead will be long and taxing for your party.
Once inside the dwarvenr ruins / troll lair, you’ll find a detailed walkthrough at Troll Trouble - Troll Lair and Troll Trouble - Troll Lair Depths. For the purposes of Harrim’s companion quest, however, the room you need to be concerned about is the throne room of the Troll King, located in the far north west of the ruins. Once there, you will see an anvil in the centre of the room. Once Hargulka and Tartuk are defeated (see here for the battle strategy), you will be able to interact with the anvil unhindered.
Regardless of your dialogue choices at this point, Harrim will be determined to destroy the anvil. Doing so reveals an artifact known as the Heart of the Anvil. Harrim has no interest in this, but you can choose to keep it to sell for a generous 500 gold. Whatever your decision, once Harrim is done with the anvil, the quest will complete. You’ll find an exit from the ruins to the southwest of the throne room.