Speak to Father for your first official Institute quest. He will direct you to meet up with a Courser at the far east end of the map, easy to reach with the waypoint indicator. Depending on how much you've served other factions, you might find the Courser in the middle of a firefight. Help him. He won't speak to you until all nearby hostiles are taken care of.
The Courser is essentially tagging along as muscle as you try to shoot your way past Raiders in a floating community in Boston Harbor. Your target is a rogue Synth. The waypoint indicator will lead you to a makeshift tower formed on top of a sunken ship. Make your way up the tower to reach the Synth. Be mindful of the homicidal Raider armed with a rocket launcher. Before you enter the top of the tower, the Courser will advise you on the best course of action, which is to read out the Synth's reset command. This is the path of least resistance.
Now with the Synth shut down, you can return to The Institute and report your mission to Father. He will then reward you with your own room. The Courser will be waiting there to give you your next mission.