Skyrim: Talk to the Jarl of Whiterun (with Video)

To talk to the Jarl of Whiterun you must first travel there from Riverwood. Across from Avalor's house (the guy who is smithing) there is a shop. Go inside it and you see people arguing. They tell you that something has been stolen from them (a golden claw) and that they want it back. Offer to get it back from them. Make sure you buy Clairvoyance from him (it comes in handy, at least when it works). Then go outside and the lady will take you to the bridge. From there you can head to Bleak Falls Barrow or go up the river to "discover" Whiterun.