- Note: Completing this quest will enable the events found in the Dragonborn expansion, where the Dragonborn gets attacked by cultists.
After battling the dragon at the Western Watchtower and returning to Jarl Balgruuf, he instructs you about the loud Dovahkin shout that you heard on the way back. He states that it's a call from the Greybeards at the top of High Hrothgar.
To reach High Hrothgar, you first need to head to Ivarstead. If you haven't visited that place, there are two routes there, either taking either the northern or southern path around the mountain. If you have the clairvoyance spell, it will direct you along the southern route through Helgen and the Alchemist's Shack. If you believe the northern route is faster, you would go pas teh Baltheim Towers. You could also attempt to take a carriage to Riften and backtrack by walking.
When you reach Iverstead, there's a discussion at a bridge just before the mountain's steps. You can speak with Klimmek for a quick quest to deliver supplies on his behalf.
When you ascend the mountain, there's a few wolves in the route, which shouldn't be too difficult. There are also various elmblems, which give a benefit if they're all activated where animnals won't attack you for 24 hours.
When you see Karita (near Emblem IV), there is an upcoming frost troll which is rather dangerous for low-level characters. It can only be avoided by sneaking past it, or by using the mountain climbing trick.
When you reach High Hrothgar, you will be greeted by Master Arngeir. After speaking with him, use the unrelenting force shout to prove that you're dragonborn. The Greybeards will then tell you about being dragonborn, and give an extra word for the Unrelenting force shout. You are then given practice targets to destroy, where you can hold the shout button for the more powerful blast.
After destroying the targets, head outside at the back. Master Borri will teach you one word of the Whirlwind Sprint shout. Once you finished the quick practice with the shout, he will instruct you to retrieve The Horn of Jurgen Windcaller.