To start the quest, the Sole Survivor must talk to Sturges, who will ask if they're willing to do some work. If they agree to help, Sturges will offer a series of four tasks to complete for the settlement: providing beds, water, food, and finally defenses for the people of Sanctuary. The Sole Survivor will need to use the settlement workshop to build the appropriate settlement buildings to provide for each need. As they build, the Pip-Boy will track their progress. After completing each objective, the Sole Survivor will need to speak to Sturges again to receive the next one (even if they build everything ahead of time). After the final objective is complete, Sturges will thank the Sole Survivor, ending the quest.
When building beds, they must be inside a building to count towards the quest. The houses in Sanctuary that still stand can be used for this purpose, or the Sole Survivor can build their own using the workshop.
Water pumps are the easiest way to provide water, requiring only a bare patch of dirt. However, at least two are needed to complete the quest due to their low water output. Water purifiers provide significantly more water, but must be placed in the river and require a power source.
In order to plant crops, the Sole Survivor will need to obtain the associated food item. Wild variants do not count. There are several crops behind the yellow house in the middle of Sanctuary that can be harvested to obtain the required materials. A settler also needs to be assigned for the crop to count towards the food supply. Unassigned settlers will typically assign themselves to tend crops, but this doesn't always happen, so it's a good idea to double-check.
A single turret will provide enough defense rating to complete the quest. The guard post is cheaper to build, but at least 3 are required and a settler must be assigned before they will contribute any defense. More defenses may be desirable to better protect Sanctuary from hostile attackers.