In order to obtain this Trophy, you need to complete the side quest Sanctuary given to you by Preston.
Following the When Freedom Calls quest, Preston asks you to check with Sturges about Sanctuary Hills as a settlement. Surges will give the Sole Survivor several tasks to complete in order to make it a proper settlement.
Craft 5 beds
Create a water supply
Create a food supply
Establish defenses
There will be enough resources around Sanctuary Hills to scrap for resources to meet the demands for all of these tasks. For the food supply, you can journey to the nearby Abernathy Farm to gather seeds or plants. Both guard posts and machinegun turrets will be sufficient to produce an adequate defense rating.
Once all of the tasks have been completed, return to Sturges one last time. This will finish the quest and unlock the Trophy.