You'll have to complete this quest to gain "The Berserker's Trust" completion, as it's required as a test to help gain Rat's Trust, so you can access the upper portion of the fort. Here's a guide to what you need to do for the Baxter's Propaganda Mission.
Wulf is not far from Chloe's Bar (you'll run into this for the quest "Unwelcome Morkon") and he'll be yelling at you to help him as you approach. Talk to him and complete all the prompts, then accept his request for help and he'll hand you two items. Open your inventory, inspect them, and talk to Wulf again to answer questions about them:
- Nail - "Looks like this nail was made in a forge"
- Flyer - "The back of the flyer is kind of interesting"
- You'll gain 100xp for answering both correctly.
Once you've answered - he'll give you his suspects, Chloe the Inkeeper and Lasse the Blacksmith. It's time to go talk with both.
Baxter's Propaganda - Chloe
Head straight over to Chloe's, and show her the Flyer - but whatever you say to here past that doesn't matter. She'll inform you that while her menus have been going missing, none have in the last week.
Baxter's Propaganda - Lasse
Make your way over to Lasse and talk with him, and ensure you have a beer in your inventory - he'll ask if you have one, and you can give it to him. He'll like that, and you can continue the conversation - which will let you show him the nails.
Once you show him, he'll say he stopped making nails because they kept being stolen, similar to what you heard from Chloe.
Before leaving - you can ask him to forge you a special weapon, and he'll give you the "The Weapon of an Artist Quest." too.
Baxter's Propaganda - Checking in with Wulf
Head back to Wulf now, and share what you found, he'll be stumped, so you put your heads together to figure out the next steps. He'll have you poke around the fort after dark to catch someone in the act - there's a small house nearby which you can sleep in for free, sleep until midnight, and head back to Wulf.
Heading out on patrol, you'll find a few people of interest - but nothing that leads to the answers you seek. Wulf heads to the bar, but you now have an area of interest on your map - head there.
Once you get there, someone named Skinny will say he has to talk to you. Follow him, and he'll explain who's to blame and he'll have an offer, and 500 shards.
If you'd like to stick with The Berserkers, make sure to head back to Wulf and tell him what you've found. He'll tell you to play along and find out who all is involved. Or, head straight to Skinny. Either way, you're headed back to him.
Thieving for Skinny Mission
Head back to Skinny and say you'll work with him, but he'll have you steal something for him before you can go any further. This gives you Thieving for Skinny mission and sends you to the upper district and a secret entrance. Head in and steal the signet ring on the table, then lock the secret entrance behind you.
The Mole's Lair Mission
After you complete the Thieving For Skinny mission, he'll take you to a trap door to meet the mysterious leader of The Claws. Follow him, and enter the trap door. Watch out, it's a long way down.
Once you're down, say hello to the leader, Yasma. Hand over the ring when she asks to keep working on gaining trust. When she asks - tell her the truth - the Berserkers sent you. She'll appreciate that since she already knew. She'll give you one final test - to plant some propaganda and tell Wulf where it is.
Now - you have two choices.
Choose The Berserkers
Give Wulf the real location, and he'll give you some shards and his trust. You can head back to Fenris for "The Berserkers Trust" and he'll grant you access to the Upper District, and Rat.
- Reward: 1000 Shards
Choose The Claws
If you choose the Claws, you'll give Wulf the information Yasma told you to give him. He'll see this as completion of the mission, and re-grant access to the upper district, letting you proceed in "The Berserkers Trust."
Head back to Yasma in the hideout now, and she'll tell you all about The Claws and their mission. You'll still need to become a member of the Berserkers, as they need more information, but you're now a member of The Claws (basically the Thieves Guild) and have access to new missions from them.
- Reward: 100 Shards
From here - if you choose The Claws, you'll want to join the Berserkers and over time you'll find out what The Claws have in store for you. Next Up: "Thieving for Yasma" and (should you join the Berserkers) "On The Road to Becoming a Warrior"