During the conversation with Tealdor (M1,7), the guard captain, you will learn that he is searching for thermal pearl. It is said to be located in the Longwatch Falls. You must go there and find it. The questgiver will also suggest you meet with an experienced hunter, Thyrsc, who can be found in his cabin (M1,3) in the same settlement. He will give you two Potions of Mirrored Image which adds +25 to deflection for 60 seconds.
Move to Longwatch Falls and go in the northwest direction. After a while you will meet a pretty large group of lagufaeths and frozen ooze, so be careful and try avoiding fighting all of them at once. Once you reach the Hot Springs (M3,2), you will meet a very large group of enemies and their leader - the Lagufaeth Broodmother. It will be a pretty hard battle. Not only will you fight few enemies at once, but they will be also healed by their mother. The best tactic is to successive eliminate all enemies, starting with the weakest one. The mother should be left for the end.
Now search through all the neighboring lakes. No matter in which order you check them, the Thermal pearl will be in the third of them. After a while a small lagufaeth will hatch from the pearl. He can be your pet now and travel with you through various locations. Go back to Tealdor in Stalwart village (M1,7). He will want to buy the pet from you for 500 pieces of gold. You can agree or keep the pet for yourself. The decision will have no additional consequences. The quest will end successfully.