There are five of them, and not all of them will be obvious gears. Here are the pieces you need and where you found them:
Happily, you don't have to figure out where each one goes; just click them in the puzzle, and they'll slide in place.
The door with the gears then slides up to reveal a box with two MORE puzzles. Oy!
How do I open the box with the green fish?
How do I open the box with the circles and squares?