If it is a major service like DHL or FedEx, the shipment will have a "tracking number" and you can "track" the shipment on a website, or via an automated telephone service. You enter the tracking number and it gives you the expected delivery date and detailed information about the status. So, personally I would ask "Can you give me a tracking number for the order?"
Otherwise, kenneth's answer is good.
Your own answer would be understood without difficulty.