Before you take on the first mission from inFamous Paper Trail, make sure that you have created an account at http://infamouspapertrail.com/ and that you have linked it with your PSN profile. The mission in question should be unlocked after completing the main mission 7a (Trash the Stash) or 7b (Fight Intolerants), that is just before heading to the south part of Seattle (Mission 8 - The Test). Look for the newly added yellow marker on the map and head there.
The starting point for missions from inFamous Paper Trail is the metal construction with two neon signs on its sides, as shown in the screenshot above. It is located in Pioneer Square district, specifically in the same place where Delsin first meets Fetch (which happens during the main mission 4). Go to the yellow marker and confirm your willingness to start the adventure, which will launch a cut-scene involving a mysterious "paper rabbit."
The aforementioned person, who is endowed with supernatural powers, tries to escape. Start a pursuit, during which you should have Neon category active, so as to be able to use Light Speed ??ability and reach rooftops of adjacent buildings more easily. No need to hurry though, as the escapee is regularly stopping, so Delsin could catch up. The chase is relatively long, although nothing extraordinary happens in its later phase.
The pursuit comes to an end in the south-west corner of Paramount district, as Delsin reaches a crime scene. Take the phone out of the inventory by pressing up on the D-pad. You have to take photos of three important areas related to the crime scene. These are namely: the roof, the person murdered, and the green traces guarded by the police in the square in front of the building.
Approach the police officers who are guarding the area. If you play as villain (evil karma), you can kill them and examine the crime scene undisturbed. However, if you play as hero (good karma), leave them be and quickly steal the wallet shown in the above screenshot (press the touchpad). Quickly retreat after successful theft, because law enforcement officers may soon start shooting.
You must now get to the roof of the theater next to the crime scene. Examine the roof, so that the main character found an origami dove. Finally, jump off the roof, stand in a designated location, and transfer all the collected traces into your inFamous Paper Trail profile.
Note: Even if you have completed the above mission before creating an account at inFamous Paper Trail website, you will not lose your progress. After following all the required steps on the main website, you just have to return to the vicinity of the crime scene and find a new yellow marker.