'The way it works currently is that quests are clientside, they still take place in the world but one player in a location will synchronise entities/NPCs to other players around them.
The project is by no means finished or complete, but you can find more info at this Reddit thread, or this FAQ page. The way FV: Multiplayer works is that one player hosts an online session that others join, and the host's game-inventory, quests, etc-is constantly synchronized with everyone else's. A modder by the name of nvm_corporal has helped create NV: Multiplayer, the first-ever co-op mod for Fallout: New Vegas that lets gamers team up with friends to explore and quest together.
