A woman named Delphine has lured you to The Sleeping Giant Inn in the town of Riverwood by taking and artifact you were seeking from where it lay in an ancient ruin and leaving you a note telling you to come here. Now that you’ve arrived she gives you the item she took, and tells you that the note was a precaution to ensure that it was you, the one she was looking for, who came to see her and not an impostor working for the Thalmor.
She now tells you that the dragons that have been appearing around Skyrim are being deliberately resurrected from their burial mounds. Only the dragonborn (or someone like him) can permanently kill dragons, but she isn’t prepared to blindly to accept you as a dragonborn despite the Greybeards’ belief in you. She has a task for you that will allow you to prove that you are a dragonborn.
According the Dragonstone map that you retrieved from Bleak Falls Barrow, the next dragon will rise from a burial mound in Kynesgrove, and she wants you to go there with her and kill it. Tell her you’re ready to leave, and she will gather her things and leave the inn.
You can follow Delphine to Kynesgrove, or if you prefer you can make your way there at your own pace and possibly arrive ahead of her. As soon as you get to Kynesgrove, one of the villagers will run up to you saying that a dragon was seen flying over the burial mound and that you should get out of town.
Delphine will run up ahead of you to the burial mound, afraid that you’ve arrived too late. Follow her, and upon arriving at the site, you behold the dragon Alduin, who is in the process of using his Thu’um to resurrect the dead dragon. Alduin will speak to you in Dragon Tongue and then in the Common Tounge, and comments that you are unworthy to bear the title of Dovahkiin because you cannot understand the Dragon Tongue. He then orders the newly resurrected dragon, Sahloknir, to kill you, and flies away.
Fight and defeat Sahloknir and absorb his soul, then speak to Delphine. She is now ready to tell you everything you want to know, and reveals that she is one of the last members of the group known as the Blades. She then goes on to say that the Thalmor are her prime suspects for orchestrating the current situation with these dragons, as they would stand to benefit from the consequences of their attacks on settlements across Skyrim.