I was wandering around south of The Castle, when I heard a strange voice of a teenager come from somewhere. Then I found that it was coming from a fridge.
-Billy says, "let me out... Shoot the door open with your gun or something!"
-Shoot to sealed door off with any sort of gun.
-He thanks you and asks you to bring him to his home.
-You accept to take him.
-On the way, you see a man by the name of Bullet approach you. He asks you to sell the child -- so you can either accept the trade or decline. (Or you can just kill him, which will help for later.)
-make your way through Neponset Park without getting killed by Mirelurk Hunters, Softshells and Kings.
-Once you've either killed or just made your way around the Mirelurks, now you have to be careful of the Raiders in Quincy Ruins. (Keep in mind, there's this Raider that's name is Tessa with power armour on and it took me around 20 minutes or more to kill her.)
-Follow the marker on your map and then you'll find yourself at the Peabody home.
-Billy reunites with his mother and father and its a happy ending.

*This is if you didn't kill Bullet/Sell Billy*

-Bullet yells from outside demanding the trade offer again.
-Decline and if you have good Charisma in this game, you can say, "They're not here!" and then he'll simply just leave. (If you don't have high charisma, you might just have to kill him lol.)
-The father of Billy pays you caps and then that's the end of quest!
(Hopefully I didn't make this guide too confusing!)