This is triggered the first time you arrive in Diamond City. Upon reaching the gate, you'll find Piper. Talk to her to trigger a cutscene. After the gate opens, follow her inside. Have a conversation with McDonough as well. After the cutscene, this quest will become available.
You just need to go to Piper's office in the market area called Publick Occurrences. Agree to have an interview with her and just answer her questions as you see fit. Once done, the quest will be complete and you'll be able to have her as a new companion.