Once you get into the most recent memory, head downstairs and exit the house.
Take the path on the left side of the front lawn and head up towards the lighthouse. You'll find your client, Johnny, sitting there with Lily.
He'll then drop the bi-colored paper rabbit on the ground right in front of him. Approach the rabbit and interact with it to start the puzzle sequence. I should mention this now, To the Moon is not a game in the conventional sense. It's an interactive novel, you will be sitting there watching cutscenes more than you'll be playing. I do, however, promise that it's worth it.
Okay, to solve puzzles we'll be going by the color of the orbs. and if it's diagonal or horizontal. The first puzzle is easy. First click the green button at the bottom, then the yellow one also at the bottom.
After solving the puzzle you will unlock the memory and you can now go back to Johnny's older memories. Examine the origami rabbit again and move on to the next memory.