Simply put, this quest involves you rescuing a kid from a locked refrigerator. To find the fridge, travel south of University Point and east of Jamaica Plain (refer to the above image for visual clues of the appliance's surroundings). You'll know you're close when you heard the kid in the fridge. Next, shoot fridge door. The kid's name is Billy, by the way.
Freeing him is one thing. Getting him home after two centuries is another matter. Follow the waypoint to his home south of Quincy. You're welcome to shorten the journey by fast travelling. Expect some Raiders as you get close to the house. Billy should be easy to protect, given that he tends to run a swift 100 yard dash away from any action and returns after the coast is clear. You can enjoy a very, very brief respite when he reunites with his now-Ghoulish parents.
Out of nowhere, a group of Gunners led by a guy named Bullet asks to buy Billy. Your choices are as follows:
Betray Billy's family, and sell Billy for a reward.
Pretend to betray Billy's family, ambush Bullet's gang and get a reward from Billy's dad.
Tell Bullet that Billy and his family are under your protection. Kill Bullet and his gang and get a reward from Billy's dad.
Any of those choices will conclude the quest.