Like all other ownership-type quests, this one is randomly triggered by talking to Preston Garvey upon the conclusion of another quest or by listening to Radio Freedom. Even if you happen to be in the middle of other quests, this quest type is worth the 10 minute detour, especially when you already have experience building essential resources for settlements.
To start, travel to the randomly designated settlement and ask the marked settler what they need. It will be one of three resource types: water, food or power.
Using workshop mode, build that resource type as many times as needed to fulfill the requirement. Report to the settler then report to Preston for your reward (which is usually 100 bottlecaps).