Once you pick up a puzzle piece the word "puzzle" will no longer be grayed out. If you the owl mask, then you'll notice little pink squares sometimes lying on the floor.

I know that the first puzzle piece is located in the Metro chapter. To get it, go up as you enter the building and take a left. Once you are near the train tracks go down. If you are wearing the owl mask ("an eye for secrets") then you'll see a little pink blob. Go to it and try to pick it up using the right mouse button.