I am new to this all and definitely lost down the yellow brick road. I clicked on the fulfillment tab thinking it would put the order into motion, not knowing it would close the order as if it's taken care of. What can I do to help my customer get their order?
You can unfulfill the item in the order details page in Shopify.
As for getting the item to your customer, contact your dropshipper. They can advise you how to correctly submit orders to them (different companies have different policies). And they can put your order into motion.