To start the DLC, go to the Abandoned Brotherhood of Steel Bunker marked on your map. Note that you will be stripped of all your items so don't bring anything; you'll thank me later. Fall for the obvious trapped radio to begin the DLC.
Once inside the DLC, you will need to save three other captives:
Dog, a schizophrenic Nightkin
Dean Domino, the performer turned ghoul
Christine, mute Brotherhood of Steel Scribe.
Your first rescue should be Dog because you'll need some essential supplies in the police station. Avoid any ghost people along the way if possible and enter the station. Once inside, you'll need to shoot radios that block your advance into the basement. Radios with a blue light and old-style radios can be shot, radios with a red light are invulnerable. Once downstairs, make your way to the recording and pick it up (also don't forget about the contraband room). Go back to Dog, play the recording, and then finish the conversation to free Dog. For a full, detailed walkthrough, check here.
Next on the list is Christine. She's trapped in an auto-doc in the clinic in the medical district. Make your way first to the medical district, then use the roofs to find the clinic door. Once inside, first go to the basement to disable the radios, and then back to the first floor to free her. Talk to her and she will also return to the fountain. Note that you shouldn't return the hologram security to the first floor; it will make the task much harder For a full, detailed walkthrough, check here.
Lastly is Dean Domino, holed up in the residential district. If you don't have the Light Step perk, you are headed for trap city. Almost every turn and stairway will have a trap on it, so keep your eyes peeled. Once you finally reach Dean, agree to be his partner. However, he will still refuse to go back to the fountain. You will need to escort him back to the fountain yourself instead. For a full, detailed walkthrough, check here.
Once all three are back at the fountain, talk to Father Elijah and the achievement should pop.