You’ll only start this quest by stumbling upon the Collective base itself, which is located in the same cave that the quest "The Baryte Rush" takes you to. This cave is south of the Sulfur Springs Forward Station, just east of a comm tower on the slope of a mountain. Explore the caverns until the last fork, where the eastern branch takes you to the objective for "The Baryte Rush". Take the branch to the south, southwest instead and you’ll eventually come across a door, beyond which you’ll meet some unfriendly - but not immediately hostile - Collective forces. After some chatter they’ll reveal the Charlatan’s disposition towards you and allow you to explore the base freely.
To complete this quest you need merely talk to the base’s commander, Crux, but there’s a bit of exploring and looting worth going over, first. Leave the base and leap up the ledges leading to the door and turn west to find a relatively small passage. Kill the Wild Adhi guarding the passage, after which it’ll open up into a small chamber where you’ll find the Datapad "Report: Generators", a container and a Lithium deposit.
In the base’s home cavern you can find another Lithium deposit just beyond the door, before the ledges that lead down to the depression in which the Collective base is built. Another Lithium deposit can be found on a ledge to the east, overlooking some Adhi Kennels, which can be scanned for some Research Data and some chatter. A container and an Iridium node can be found southwest of the base, behind a pillar, just west of a bridge near which you’ll find the Datapad "Latest Shipment". Southeast of this bridge (and the base itself) you’ll find three more containers and a Titanium node behind another pillar. Northeast of the base you’ll find yet another Lithium deposit behind some rocks, near a stalagmite, while another Iridium node can be found to the west of here (northwest of the base), near some crates. Finally, just east of the base you’ll find an Iridium deposit, just sitting out in the open.
Make your way over to the base itself, or rather, under the base, as you can find a Salarian guarding a "Mysterious Button". You can waste your time and aggravate/amuse the Salarian by repeatedly pressing the button. Head upstairs and make your way to the southern walkway to find a Thruster you can scan for some Research Data points, then head inside the lower level of the Collective base itself to find a container and the Datapad "Personal Log: Aquila".
Next head to the top floor of the Collective base, where you’ll find Crux’s office. Crux is here, of course, but before you bother her interact with her Terminal and pick the option "Unlock Holding Cells". Leave Crux’s office and drop down to the ground below the base, then head east to find a door beyond the Salarian and his "Mysterious Button". Open the door, beyond which you’ll find some holding cells, where a Collective agent is busily roughing up some prisoners. Talk to the Collective Guard and make whatever call you wish about the tor… err… "enhanced interrogation", then read the Datapad on a crate and loot a Titanium node.
Finally, when you’re done with all this return to Crux’s office and talk to Crux to finally end this quest and begin the quest "The Charlatan’s Charlatan".