When you first approach the New Camp you'll come to a bridge that turns out to actually be a dam. A man named Homer is standing on it, staring out into the distance. He explains that a Lurker is gnawing at the foundations, threatening to flood the rice fields below.
Turn around so the dam is to your back. Over to the right you'll see a shoreline that goes around, and then a giant rock outcropping more to the center of the lake. Follow the shoreline until you reach the rock, where the Dam Lurker prowls. If you have the power, kill it. If you don't lead it back the way you came. Any time it makes a different growling that means it's turning around and giving up, so go back and entice it towards you again.
When you reach the dam turn right and go up towards the city, then turn left into the cave, all the while ensuring it is still following you. Most people will run, but the stronger or named NPCs will attack it for you and soon kill it. Do not save your game just yet! Investigate its corpse and grab the Dam Lurker Claws. Now head back to Homer and tell him you killed it. If you can't find Homer, look over the edge of the dam; in his panic it is possible Homer may have decided to jump, and if he did this quest can't be completed (load your last save if this is the case). Once you've reported your success to a definitely alive Homer it's safe to save.
Early in the game, the Dam Lurker may be difficult to fight directly (your weapon not doing enough damage, etc.) but you can use a bow and arrow to kill it, giving yourself the experience for killing it AND completing the quest. The Dam Lurker is much like a normal Lurker in that it has a lower tolerance against arrows (20) than melee (50). The trick is to walk up to where the Dam Lurker waits, draw the bow, and fire arrows until you hit it. When it gets too close to you, jump-run away until the Dam Lurker can no longer be seen (almost near the Peasant's communal hut, usually); watch out for the trees. Now, walk back to find the Dam Lurker in its original position and with that much less health. Keep employing this strategy until the creature is dead. This strategy was designed to make use of Mordrag's Ring and the Rider's Bow and arrows locked in a chest above the New Camp entrance lookout structure (essentially, free items).