These are the ways I got the achievement. There may be others as well.
* Medical - Talk to Doc Parker in the Colorado Springs garage. He will ask you to help three patients laying in the makeshift hospital, using the First Aid skill and one each of a Suture Kit, Injury Kit, and Medic Pack. After you heal all three patients, he will join you.
* Museum - Talk to Jumko Murayama outside the front entrance to the Patriarch Museum in Colorado Springs, after completing the "Cornered Rats" quest in the Garden of the Gods. There is a conversation option for her to join you.
* Brig - Hope Emerson will join you as a quest reward for completing the "Cornered Rats" quest in the Garden of the Gods. Speak to Sheriff Daisy in Colorado Springs to complete the quest and she will offer Hope's services.
* Armory - Inspector Delgado will join you as a quest reward for completing "Big Trouble In Little Vegas" in Colorado Springs, if you side with the Marshals and arrest Brygo Faran. If you side with Brygo, he will offer someone as well.
* Garage - Someone will join after completing the "Unwanted Guests" quest. The quest is given by Gideon Reyes in the Broadmoor Heights church. He will contact you by radio to start the quest, and will send you to the Bizarre to deal with the flow of refugees.