Mind the (Fence) Gaps
Start by talking to Captain Lawgof. He will offer to make you an honorary member of the Black Guard. He will give you 6 railings and a hammer, asking you to fix the gaps in the fence.
Click on each broken railing to start trying to repair it. After you've repaired them all, talk to the Captain again. He now wants you to check on the watchtower to the south.
Checking the Watchtower
Head south a little bit to find a wooden watchtower. Climb up the ladder, and go to the top floor. Take the dwarf remains in the corner and return to the Captain. They took the dwarf's son too, and the captain asks you to retrieve him.
Follow the path south, then east around the fishing guild. Near the windmill east of the fishing guild, look for a cave entrance. Go to the far northwest corner, and look for some crates. Look for the below crate on the east side of the room.
Return to the captain at the coal carts. He now asks you to repair the cannon.
He will give you a toolkit. Use it on the nearby cannon. Use the rightmost tool on the spring, the middle tool on the safety pin, and the leftmost tool on the bottom gear.
He now wants you to go to the Black Guard outpost on Ice Mountain to find out what it uses as ammo. Once at the dwarven camp, enter the middle building, the one east of the machine building.
Speak to Nulodion there. He will give you an ammo mould and instruction manual to give to the Captain. Return to the coal carts and talk to him to finish the quest!