Proving Honor is the second of the main companion quests. It is available after the first companions mission (usually given by Farkas), and given by Skjor.
When you speak with Skjor, he will mention that a fragment of Wuuthrad, the Blade of Ysgramor, is in Dustman's Cairn. He will have Farkas join you in the quest, with your existing follower being sent back to the home location.
Dustman's Cairn is north west of Whiterun, about half-way to Morthal. It is very close to Hamvir's Rest, and it is very easy to activate the undead waiting that that location.
Dustman's Cairn[edit]
The first few rooms of Dustman's Cairn are devoid of enemies, save for the ones already slain. Of note, the first room has a two-handed skill book.
The tunnels ahead will have your first Draugr in a small group.
When you reach the large room, you will have to enter an alcove and pull the switch. This traps you in the alcove, and Farkas will head to release you. In the cutscene, you will see that the Silver Hand had performed an ambush, with Farkas revealing his werewolf form to escape. Once you're free, he will explain the situation, and encourage you to keep moving - although you can examine the corpses to retrieve the silver swords (which tend to be the most valuable large item at low levels)
The enemies are mostly silver hand, and there's no special issue advancing through the rooms.
Dustman's Crypt[edit]
When you enter, the Draugr and silver hands fight amonst themselves, making combat slightly easier. The tunnel leading down will have some draugr in their alcove, and one of them may wake up when you pass.
In the first room, you should see an adept-locked door containing some ingredients, and an adept-locked chest.
Continue to the next room, and search the chest on the left to get the Dustman's Cairn key. This allows you to get past the door.
There is an alchemy lab in the next room, but nearby skeevers prevent you from using it until they're defeated. The locked door contains ingredients. Remaining enemies should just be a few Draugrs.
In the room with the fragment, there is a word wall that lets you learn Fire Breath. Once you take the fragment, the remaining set of Draugrs will break out of their sacrophagus. They will attack a few at a time, but in a large number. When you are able, you can exit by climbing the stairs to the left of the word wall.
Return to Jorrvaskr[edit]
When you reach Jorrvaskr, Vilkas will say that they were awaiting your return. He will ask you to follow him behind the building, where the five members of the circle will formally induct you as a member.
Once again, you can speak with four of the companion leaders to get another mission.
The following part of the Companions quest line, The Silver Hand, requires you to complete one additional task.