Random NPCs give quests.
The Old Guard Rep, Old Guard Rep, and Free Merchants speaker give quests at the Evac Center.
The Old Guard Captain and Old Guard Comms Guy give quests at the Necropolis.
The Ranch Foreman, Ranch Scavenger leader, Ranch Nurse, and Ranch Bartender (I think) give quests at the Tacoma Commune.
You’re welcome to write more missions/quests: fetch quests and kill monster quests can be done entirely in JSON at this point. See The Guide for 1st Time Modders, especially the sections on NPCs and missions.