Start the quest by speaking with Theradus in the Mileth Tavern. He will tell you about the Dragon Scale sword, then suggest that he would be more likely to talk if he had some seafood. You can either board the Pirate Ship and get a tentacle, or hunt one from an octopus in Lynith Sea. If you board the Pirate Ship be sure to have a proper disguise to avoid being thrown in the brig.
When you return to Theradus with the Tentacle he will tell you to stand on the dragon's eye in Shinewood Forest 8. From SW entrance, travel north to Shinewood 5, then east to 7, and from there south to 8. Opening your Tab Map will display an invisible dragon. Walk through it's mouth and stand in the eye to summon the dragon. When the dragon dies he will drop the Dragon Scale Sword.
So you want to know about the Dragon Scale sword, eh?
Well, I already have something to drink, some food would be nice. How about some seafood? Ever since Lynith Beach opened I have been craving for some.
You have any?
Yes, here you go.
Thanks so much. Here is what I know. The Dragon Scale sword is a special sword created from the scales of a dragon. It is very durable but it is not that powerful for high insight Aislings.
The sword is guarded by, of course, a dragon within Shinewood Forest. I do not know exactly where, but there is a clue, hmmm... Ah yes, now I remember, "To get the sword, walk into the mouth of the dragon and stop on it's eye." That's all I know.