This quest can start in one of two ways: you can either talk to Lucan Valerius, the owner of Riverwood Traders in Riverwood OR you can enter the 'Bleak Falls Barrow' dungeon and OVERHEAR the bandits talking about the claw they stole and get the quest that way.
This quest is tied DIRECTLY with the MAIN STORY MISSION ‘Bleak Falls Barrow’ , and in order to better serve yourself you should really complete both of these quests at the same time. You can find this main story mission underneath the main story questline. It’s the third quest in, you can’t miss it.
Skyrim is the homeland of the Nords, a fierce and proud warrior people who are well suited for the bitter cold and mountainous terrain which defines the land. Now scarred by civil war, Skyrim faces its darkest days with the return of the legendary dragons and their leader, the World-Eater Alduin. The future of Skyrim and even the lands beyond hangs in the balance, as the people await the prophesized Dragonborn, a hero born with the power of The Voice and the only one who can contend with the dragons. You are that Dragonborn; your task is to investigate why the dragons are returning, and discover a way to defeat them. At the same time, you’re free to explore Skyrim at your own pace, uncovering its many wonders along the way.