Learning of the Squire's Mishap
Speak to the squire located in the White Knights Castle courtyard. Ask him how life is as a squire. He will tell you about his mishap of losing Sir Vyvin's sword. Tell him that you will make a new sword for him. He will then reply that is it basically impossible since the sword was originally made by the Imcando Dwarves five generations ago. Tell him that you will track down the Imcando Dwarves tribe.
Head to Reldo in the Varrock Palace Library. The library is located in the northern side of the palace. Ask Reldo if he knows anything about the Imcando dwarves. He reveals that there are a few surviving in the southern peninsula of Asgarnia and that they REALLY like redberry pie.
Creating a New Sword
Speak to Thurgo whom is located by his hut just south of Rimmington. Ask him if he would like some redberry pie. He will quickly take it off your hands and eat it. Speak to him again and ask him to make you a special sword. He needs to know exactly what it looked like before so he can make a new one. Head to the squire and ask if he has a picture of the sword. There is a picture of Sir Vyvin's father holding the sword located in Sir Vyvin's cupboard. Sir Vyvin's room is located on the third floor (second floor for the British). Search the cupboard and then take the portrait, grab a pickaxe, and head back to Thurgo.
To make the decorative sword Thurgo needs two things: 2 iron bars; and a special ore, blurite. The only place to get blurite ore is under the cliff which you are next to.
Head up to the top of the cliff and climb down the trapdoor. Run all the way to the area with the ice warriors and mine the blurite which is located on the east wall. Make sure you turn "Auto Retaliate" off so it makes your run easier. Low levels are advised to bring food. You can and will get killed in the ice dungeon. Once you collect all the materials take them to Thurgo and he will make the replacement sword.
If you wish to make and keep a sword for yourself collect extra supplies and drop the current sword on the ground. Ask Thurgo make another sword for you then simply pick the first one back up again.
Take the sword to the squire and...