At the top of the stairs, you will need to head over to the right. Go on up the stairs. Move in carefully. There can be guards in this area, and without having done any favors for the Jarl of Markarth you will be trespassing. You will encounter a locked door (Adept) which is blocking your way into the area.
Inside the room, go straight across to the dresser. Open it up and claim the Raerek's Inscribed Amulet of Talos.
With the Inscribed Amulet in hand, head on out of the room. Go to the center of the Keep and approach the Jarl. You want to talk to the man on his right, Raerek. Show him the amulet and he will tell you to follow him somewhere. Stay somewhat close to him to avoid having the guards questioning you. He will only start moving after all his scripted conversation is complete with the Jarl (if this is your first time inside this location).
Follow him back to his room where he will be able to tell you more. You can also about why he does not join the Stormcloak rebellion. To move things forward, get to the Perhaps we could come to some kind of agreement option. Agree to the deal (or with a persuade you can get some gold out of him using a different option).
Report to Galmar Stone-Fist
Leave Markarth for the Stormcloak camp. Once there, approach Galmar Stone-Fist and tell him about the information you got. He will tell you that he has some men who are headed in that direction. You just need to meet up with them.
Meet the men
Head to the Southeast from the camp. It is only a short run over there.
Head along the path past the Broken Tower Redoubt. Continue to the East along this road and you will see the troop you are looking for in the bushes off to the left of the road. Leading them is Ralof. Talk with him to trigger the next part of the quest. He will propose a plan where you help him and his team ambush the caravan. You also have the option of telling him and his men to wait there until you call for them.
Take over the Caravan
There are a number of ways to approach the camp. Having anything that boosts damage against unaware opponents is very helpful.
If you want to follow the plan with Ralof, you will need to head up the slope and then eliminate the Scout there. After that, the Stormcloaks will take position on the slope above and start firing arrows against the Imperial troops below them.
Return to Ralof and report your success.
He will then send you back to the Reach Stormcloak Camp. The quest is complete.