To use your Fridge, simply select the item you want to store then drag and drop it to the Fridge icon in the bottom-left of your screen. If the item returns to your board when you try to do that, then you might not have enough slots. In this case, you can use Gems to unlock more slots.

To move an item back to your Board, just open the Fridge and tap on the item. Also, whenever an item is needed for one of your orders, and it is located in the Fridge, there is no need to move it back to your board as it will automatically go towards that order.