Agarth awaits you on the Didenhil tavern M3(6). He will give you a fire protection ring and let you choose how to enter Tuath's hideout M3.5.
You can either attack from the front (western entrance) or sneak in from behind (eastern entrance). The first option includes more fights and the second a tunnel filled with traps.
Hunter's Pit map
1 - Traps
2 - Beasts
3 - Eyes of Tirnoch
4 - Back exit
5 - Front exit
If you decide to sneak in from behind, head any way you like after entering the cave. Both paths will lead you to the destination point marked on the map.
Don't forget to disarm the traps on your way and freeing the beasts that will help you fight with the Tuatha. Reaching the mentioned chamber also requires lockpicks, using which you will be able to open the locked gate.
By choosing to attack from the front, you will have to be ready for more fights. Enemies will await you behind almost every corner and in big groups. In this case however, you don't have to worry about any traps.
After finally reaching the destination, defeat all the enemies together with Agarth and afterwards approach the Artifact do destroy it.
A short conversation with Gadflow will commence. Afterwards speak with your companion.
Before leaving the dungeon with him and ending the mission, I'd recommend searching the second part of the cave. You can find quite a lot of treasure there.