Fast travel to Riften and enter the Mistveil Keep. In here, you'll see the Jarl of Riften, the Stewart and two guards guarding the door behind them. Inside this opening, there's another guard patrolling. Wait for him to go left, enter sneak mode and sneak to your right, entering Anuriel's room. In here, loot everything and leave the dresser for last.
Take the Incriminating Letter from the dresser, approach the door and wait for you to hear the guard's footsteps. When they fade away, open the door and leave the room. Now speak to Anuriel next to the Jarl and show her the letter. She'll have you follow her into her room, so do so. Once here, tell her what would happen if the letter was made public.
Ask her what kind of agreement she has in mind. She speaks of Gold and Weapons. Tell her you want something for yourself right there, right now (This has a chance of netting you 750 gold if your speech skill is high enough; mine was 29). She won't bend, so ask her further info and then, report back to Rikke. Afterwards, its time for you to meet the other soldiers. Fast travel to the closest location. Once you reach the marker, which is Hadvar, speak to him and when ready, sneak alongside him...
Note: There's 2 ways to do this next part. Once is to follow Hadvar's plan and sneak. The other is not liking his plan and going solo. If you go solo, you'll have to kill around 6 Stormcloaks alone. If you want some extra help, follow Hadvar's plan.
If you decided to follow Hadvar, then soon enough you'll find two imperial soldiers. When told, look north and kill the Stormcloak Scout. Now, you'll have to take care of the rest of the Stormcloaks. Go in there and lure them out so the imperials can start shooting arrows at them. Once you take care of them all, loot the wagon, report back to Hadvar and return to Rikke.