To trigger this quest, you first have to alienate yourself from The Institute. Simply assault any human member of The Institute (Father included). This will trigger the Banished from the Institute quest. If you happen to attack Father outside The Institute (like at the conclusion of The Battle of Bunker Hill), you won't have to complete Banished from the Institute unless you want to.
Talk to Preston Garvey, who you'll find at either Fort Independence or Sanctuary Hills. Now that you're a high value target to The Institute, Preston will urge that you help grow The Minutemen into a force that can take on Father's faction.
If you have spent any time helping The Minutemen, you should have a number of established settlements on the faction's side, thanks to various Radiant quests. The goal is to have at least eight such settlements. To do so, you just have to impress settlements by helping them out, as opposed to building recruitment beacons. The quest should conclude when you've recruited your eighth settlement.
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