On this page of the guide for TES V: Skyrim, we have presented a walkthrough of the initial part of the main quest Bleak Falls Barrow, unlocked when you reach Whiterun. Before going to the ruins, the main character must talk to Farengar.
New main objective: Talk to Farengar
Follow Jarl Balgruuf into one of the smaller rooms of the Dragonsreach. Listen to a conversation with Farengar, which you will have the chance to join soon enough (screen above). The mage will want you to examine the ruins in search of the Dragonstone, containing the map to the Dragon cemeteries. While you're at it, you can also ask Farengar some additional questions and therefore unlock some additional missions and trade with him.