Out of Time

Out of Time is a main quest in Fallout 4.

Detailed walkthrough
Essentially retrace the path the player character took to get to the vault to get back to the Sanctuary Hills neighborhood and house. Codsworth will be near the player character's home. The interaction with Codsworth serves as the dialogue tutorial.

Explore the neighborhood by following Codsworth who is following lifesigns. This will lead to combat with Bloatflies. When two battles are done Codsworth will suggest the Sole Survivor go to Concord to continue the search for Shaun.

Head past the house with the cook station. The Sole Survivor will see a bridge in the near distance. Cross the bridge.

The next location down the road is the Red Rocket truck stop. Here the Sole Survivor will encounter Dogmeat. Be sure to loot the station before heading down the road to Concord.