Head forward with your dad and exit the house. The game will of course use this first chapter to teach you some things, like how to vault over railings. Keep following him and when he tells you to stay put go ahead and do so since he'll tell you to move onward soon. You'll meet another man soon. Stay crouched by him while some Helghast soldier patrol overhead. He'll tell you when it's safe to continue.
Follow him into a room where he'll introduce himself as Shadow Marshal Sinclair. Continue on and soon you'll be at a stuck door. When you can look to the left and have your dad help you up to the room. Crouch down up here and head forward and drop down the hole on the right, then remove the plank from the door.
Continue following the two for a series of scenes...
Many years have passed. The prisoner exchange you are witnessing will soon go wrong (go figure), so be ready to grab the gun (Square) and then shoot the guard. You'll see some more scenes after that that will set up the story. Chapter 1 will then come to a close.