The soldiers of Targos seem overwhelmed by the goblin raiders. Yet even as we fight street-to-street and house-to-house, others cower indoors, seeking solace in their cups. Bah! It is good that we arrived when we did, for we will surely be well rewarded for our efforts. But I thank Tempus that my healing skills have been little needed to this point.
We met an aged dwarf in the south end of the docks - the ground about him was littered with the bodies of filthy goblins! Trust a dwarf to know the worth of those foul creatures. He was pleased to speak with both Halgren and me, and even offered us the use of his house and equipment. It was his insight that has led us to these abandoned caves. Having routed the goblins from the streets above, now we shall bury them in their holes.
Alia Shield-Maiden, the Annals of Halgren
These caves are loaded with goblins, but they have spread out so you can deal with them in small groups. The first group is just past the entrance to the tunnels. If you have a rogue or a ranger with good stealth skills (Hide and Move Silently) you might want to spend a few moments scouting out the tunnels. They aren't very big, but there are some tight corners. By scouting ahead you'll know when to expect a fight. It will also help you to avoid getting caught by two groups of goblins, so you can focus on one group at a time.
As you clear out the tunnels, you'll find a couple of places where the ceiling has caved in. It would appear that Jorun was correct and the goblin raiders did come this way. Make your way west until you come to the end of the tunnels. Here you'll find a slightly larger group of goblins, including several archers and a slightly tougher goblin named Rukwurm. After taking him out, make sure you loot his body. You'll find an unidentified scroll labelled a "Charred Vellum Scroll". Make sure you don't lose it! You can identify it yourself using the Identify spell, or you can have it identified by a merchant.
If you've already taken care of all the goblins in the docks area, when you kill the last goblin in the tunnels your journal will be updated saying that you've cleared all of the goblins out of Targos. Keep your eye out for this journal entry. It will only appear when you've killed every last goblin in the Targos Docks and in the Smuggler's Caves. You'll also get quite a nice reward (1350 xp). Completing that main quest also allows you to proceed to the next stages of the prologue.
With the tunnels cleared out, head back outside to Brogan on the docks.