After meeting the Greybeards at their mountain temple of High Hrothgar, Arngeir will give you one last task to do to prove that you are a Dragonborn: obtain the Horn of Jurgen Windcaller, one of the heroes of old. The Horn is located in the ancient Nordic ruin of Ustengrav, which Arngeir marks on your map for you.
The simplest way to reach Ustengrav is by taking a carriage to the town of Morthal, then trekking through the marshes on foot. The ruins can be found to the northeast of the town. When you arrive at the ruins, you’ll encounter some bandits engaged in combat with mages. Since both groups are hostile, you’ll likely have to mop up the survivors unless you can sneak past them all.
The first level of the ruin is fairly straightforward, with a few mages and draugr to deal with. Entering Sneak mode and following the mages deeper into the ruin rather than attacking them yourself immediately will result in an eventual fight between them and the draugr, leaving fewer enemies for you to deal with. When you’ve picked off any survivors and collected all the loot worth taking, descend into the second zone of the ruin.
Upon entering Ustengrav Depths, you will see a vast, somewhat forested chasm with a waterfall and a bridge. As there is no way down to this area, except by a steep fall that would surely be fatal, you will have to navigate a winding passageway through the rest of the ruin. There will be several draugr and a fire trap to hinder your progress along the way. In the outdoor area itself you will encounter several skeleton patrols, both on the ground by the bridge and in the higher up area with the wood barricade. These can easily be taken down with a good shot from your bow. Note that there is also a skeleton in the room with the tall pillars who is seated in the throne but will rise and attack you when approached.
Near the bottom of the waterfall is a Word Wall with the Words for a “Become Ethereal” shout. It can be seen from the bridge and is reachable via a small path carved out of the side of the cave wall. Behind the waterfall is a hidden area containing a draugr and some stashes of loot. The Horn, however, lies on the other side of the bridge, so after you’ve learned the shout and collected the loot, go back up the path and head across the bridge.
Across the bridge you might encounter a lone skeleton who is easily dispatched. The main attraction here are the three outcrops of rock carved with runes and the tunnel you need to access to continue which is currently barred with three gates. Each of the rocks glows red when you approach and lifts one of the gates closing the tunnel. Starting at the rock nearest to the bridge, sprint by each of them until you get close to the tunnel entrance, and from there use Whirlwind Sprint to clear all the gates at once. Once you are clear, the gates will remain fully open, allowing any followers you have with you to follow you in.
The floors in the next few chambers are covered with fire traps that may or may not work, and there are two spiders on the cobwebbed arch. The room beyond the arch also contains a giant spider and two of her smaller offspring. After dispatching them, cut through the cobwebs covering the tunnel and enter the next chamber.
The final room in Ustengrav contains a lake between you and the altar where you expect to find the item you seek, with a bridge for you to cross. As you approach the bridge, four Nordic dragon carvings rise out of the water, but these don’t do anything, so just cross the bridge. On the other side of the bridge lies the pedestal upon which the Horn of Jurgen Windcaller should be seated. But when you get close, you find the pedestal bare except for a mysterious note addressed to “the Dragonborn”. The note states that the Horn has been removed and requests that you rendezvous with the note’s author by renting the attic room at the Sleeping Giant Inn in the town of Riverwood.
Leave the dungeon and make your way to Riverwood as the note instructs. When you reach the inn and speak to the innkeeper, Delphine, about renting the appropriate room, she tells you that there is no attic room, but you can have the one on the left if you like. Go into the room on the left and she’ll follow you. When you’re alone, Delphine tells you that she was the one who took the Horn, and gives it to you. She asks to speak privately, and you follow her to the room you usually rent. Delphine opens the wardrobe door, revealing a stairway to a secret chamber beneath the inn, where she bends over a map on a table and begins speaking to you. She will not share many details with you, but she says that “her organization” has been looking for one such as you, and that she took the Horn in order to get you to come here. This exchange with her begins the quest A Blade in the Dark, and when you’re done speaking with her you can return the Horn to the Greybeards at High Hrothgar and complete the quest.
If, however, you first return the Horn to its pedestal in the ruins you just came from and activate the pedestal, you will be granted a dragon soul as a reward. In fact, due to a glitch, if you rapidly press the activate button several times in succession when interacting with the pedestal, you may be granted two dragon souls instead of one. When you’ve done this you can just remove it again, leave the dungeon and head off to present the Horn to the Greybeards.
Return to High Hrothgar with the Horn and present it to Arngeir, who will take it to the main hall, where the other Greybeards are assembled, and Wulfgar will teach you the last word to the Unrelenting Force shout. The Greybeards will now perform the ritual that signifies they formally recognize you as a Dragonborn, and from now on High Hrothgar is open to you.