In short: Steffen is looking for a powerful tome - Salomet's Grimoire. The NPC is pretty easy to locate - he's walking around the market during the day and the night.
Difficulty level: Medium. You'll need to break through to a Bandit's camp. Or, in harder version (optional) - embark on a journey to a far away land.
After accepting the quest, go to Camellia's Apothecary at the market. She'll point you to another destination.
Now you need to go to the Bandit's camp west of Gran Soren. You can, however, omitt this step and go straight south, in the direction of the Encampment. On your way you'll stumble upon a man under attack from thugs. Rescue him and talk to him. He'll show you the way to Aernst Castle Ruins.
The leader of the group in Aernst Castle Ruins won't tell you where he had hidden the tome. You don't need to worry about his permission, though, because...
You can simply climb a nearby tower, half in ruins. The tome is hidden in a chest on the top. Give it back to Steffen.