The quest begins by traveling to Daguerreo (click on the link for more information). Speak to the old man near the library on the third floor. He asks that if you find an item called the “Magical Fingertip” that you bring it to him.
Travel to the Auction House in Treno. You now need to purchase each of the following items and offer to sell to the each of the corresponding people below. Note that you can sometimes purchase these items and then sell them for a profit. Most of the people will offer one price and then can be bartered up to the second price:
Doga’s Artifact which can be sold to the Scholar in the Synthesis Shop. It can be purchased for around 9,000 gil and can be sold for 10,000 on the Scholar’s first offer. The Scholar will not pay any other price.
Une’s Mirror which can be sold to the Nobleman just outside the Synthesis Shop. It is normally purchased for around 11,000 gil and can be sold for 12,000 gil on the first offer or 15,000 gil on the second offer.
Rat Tail which can be sold to the Adventurer who is also just outside the Synthesis Shop. The Rat Tail is normally purchased for around 17,000 gil and can be sold to the Adventurer for 20,000 gil on the first offer or 25,000 gil on the second offer.
Griffin’s Heart which can be sold to the same Adventurer. It can be purchased for around 6,000 gil and can be sold for 8,000 gil on first offer or 10,000 gil.
Return to the Auction House after you have purchased and resold all four items and the Magical Fingertip will appear as a new item that you can bid on. It can cost anywhere from 40,000 gil to 60,000 gil depending on how lucky you get. Return to Daguerreo with the item and present it to the old man to receive the Excalibur sword as a reward for completing the quest.