This quest begins just after your first talk with Tann in his office. As you exit, you'll see a console explode. Go speak to the engineer working on it.
Raj will give you some backstory, and also point out why you are the perfect person to crack the case (is that not always the way?). He'll populate your map with markers for other tampered consoles. For each one, use your scanner on the console itself, then trace the glowing piping to the console that was hacked.
The consoles are (by order of proximity):
In Director Tann's Office, across from his desk. This leads to a console on the top level of Colonial Affairs.
Tucked away on the north side of stairs between Colonial Affairs and Operations, by some black crates. This conduit leads to panel on the ground floor in the northeast corner of Colonial Affairs.
Near the ceiling in southeast corner of the militia office. This does not link to another panel.
The evidence here will point to one Zarah Kellus. You can find her in Habitation (you'll have to take the tram to get there).
Confront her to learn that both she and Raj have been framed by a third party. Tram back to Operations to review security footage.
The files have been scrambled, but you can narrow the suspect list down to human males in Security. You can now scan potential suspects with your omnitool, but culprit will always be working back in Habitation - one Dale Atkins.
When confronted, he confesses almost immediately. You then have the choice of whether to let him flee into exile, or turn him over the authorities.
A little realpolitik here- Dale doesn't really deserve any special mercies. His actions could have killed people, and he went out of his way to frame innocents, and he has no plan for change or justice. He's just lashing out and hurting people who had nothing to do with the decisions he hates, and he's endangering the most stable outpost of Alliance civilization in the entire galaxy. On the other hand, I suspect we're going to need a friend in the Exiles at some point, so it's probably best to let him go, and just hope he doesn't steal or detonate anything important on his way out. No matter what choice you make, you still get exactly the same number of Andromeda Viability Points for resolving the mission.