This quest doesn't have a typical "completion" (no turn-in, no ding/reward). Once you build the traps, you return to what you were doing prior, but have traps to use!
The rats within this special instance of Nektropos Castle will all be 10-20 level above you (the scale).
You must sneak past the first group of rats. You have to get quite close for them to attack (aggro), so it is possible to sneak by without too much worry. To get past them to get this sub-quest, keep close to the walls.
You should already be in this zone if you have this quest, but if you must return:
The recipe for a rat trap is on the bookshelf in the forge room.
Scrap metal can be found in barrels in the forge room ( -3, 0, -28 ) /waypoint -3, 0, -28.
Scrap wood is found in the stables ( -16, 0, -9 ) /waypoint -16, 0, -9.
Something edible looking is in the kitchen ( 13, 0, -26 ) /waypoint 13, 0, -26 hanging above the fire in the pot.
Scribe the recipe and use the forge to build 20 traps. Drag the rat traps (a cage icon) to your hotbar for easy use.
Use the rat trap on the rats to maneuver around the castle and collect the items needed for Craftsman Errands. You can set the traps and pull the rats to them to speed things up, but each trap will only disable 1 rat.