Talk to Ser Maximilian outside the Gran Soren Castle Gates. Make sure you have your Wyrm Hunt License on you. He gives you choices such as the following:

Decipher a text
Rout a monster infestation
Aid a research team
Nothing for now

Choose: Route a monster infestation

He tells you about an urgent message from the Stone of the Southwest. A horde of goblins struck the fortress while it was still under repair, and they've claimed it. Though the hold is remote, its importance to the southern defenses is critical. We must reclaim it, and soon. The safety of the entire duchy rides on this matter.

Accept the quest to begin:

A Fortress Besieged
Speak with the Captain

Objective
Wyrm Hunt Quest
Goblins have seized the Stone of the Southwest. Reclaim this vital bulwark against the dragons.

Details
Travel to the Stone of the Southwest and join the force sent to recapture the hold.

Set the quest as active, and open your map to locate the destination, the Shadow Fort. The fort is pretty far away, but you can use the Ancient Quarry as a shortcut, entering from the North Entrance to the west of Gran Soren, and coming out from the Southern Entrance, east of the Shadow Fort.

Talk to Ser Robert. He wants you to spearhead their forces here. He wants you to pass through the hole behind him, and open the gate from the inside. Jump under the hole, and go through the tunnels. You will be fighting enemies such as bats, goblins, and hobgoblins. Climb up some flights of stairs. Soon you reach the gate lever, but you find out it has been removed. There is also a ballista on the wall, which you can use to shoot some of the goblins, cyclops and ogres in the area.

Then, climb down to the courtyard, and dash across to the other edge. Climb the ladder. Jump down to the Station Room. Open a door, and arrive at an area with holding cells. Open the chests there, one of them will have the Shadow Fort Lever. Go back to where the broken lever mechanism was, and open the gate. Then, help the guards rout the Goblins. You can use the Ballista again to help clear the yard.

Then, you have to defeat the Goblin Chieftain. Climb up the spiral stairs in the tower, and chase the chieftain. Be careful of more Cyclopes. Enter the Commander's Antechamber. Attack the chieftain. There is a  cutscene, and he jumps from the window.

Then, go back to Gran Soren and report your victory over the goblin horde to Ser Maximilian. This completes the quest, "A Fortress Besieged".