Return to Falador Castle, and speak to the Squire. He'll say that the portrait of the sword is somewhere upstairs in the castle. Take the easternmost ladder up, then open the door beside you, and go inside the large room. Inside, open another door to the south. Close the door behind you to avoid being seen, then
search the cupboard for the picture of the sword.
Return to Thurgo, and hand him the image of the sword. He tells you that he needs two iron bars, and one blurite ore to form the sword. To find the blurite ore, you'll need to get some armor and food ready, and enter the dungeon at the top of the cliff, just beside Thurgo's house. Inside the dungeon, make your way as far east as possible, into the icy area of the cavern. Throughout this area, you'll find blue rocks. These rocks contain blurite ore. As you avoid damage from your enemies, quickly mine one blurite ore (or two, if you wish to have your own blurite sword), and exit the cavern via the way your entered.
Return to Thurgo, and hand him 2 iron bars and 1, or 2 blurite ores. He will then make your a Blurite Sword. Return the Knight's Sword to the Squire, and you will complete the quest.