To use your Fridge, simply select the item you want to store, and then drag and drop it to the Fridge icon in the bottom-left corner of your screen. If the item is a Generator Piece and you have slots available in your Generator Storage, it will automatically go to your Generator Storage; if not, it will be stored in your regular Fridge. If the item returns to your board when you try putting an item inside, you might not have enough slots. In this case, you can use Gems to unlock more slots in your Fridge, or reach a special milestone in Edwina's Cash Dash to unlock more Generator Storage Slots.
To move an item back to your Board, just open the Fridge and tap on the item. If you cannot find the item you're looking for, it might be in your Generator Storage. To move between Generator Storage and Fridge, simply tap on the tabs. 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.