The world of Fallout 76 features no NPCs whatsoever. They have been replaced by players who play the characters they have created - you can cooperate with them, trade, fight or simply not pay any attention to them. This does not mean, however, that missions have disappeared from the game.
In Fallout 76 you can indeed perform missions - what's more, completing the missions is very profitable, because you get many useful items such as Stimpaks or weapons. Tasks are given to you after hearing hollo tapes, reading the notes or using the computer. Missions are also activated when you enter some locations. The game makes sure that you still have missions to complete, but if you want to perform additional missions, just explore the world and look into every nook and cranny.
In addition to standard tasks, you can also take part in events. They are randomly generated and can be joined by any nearby player - just get near the place. You also perform some kind of missions during events, but they are based on cooperation with other players and are mainly about repelling waves of enemies. Of course, for successful completion of the event, you receive prizes - caps, ammunition, Stimpaks or weapons.