If you buy something outside of Germany that has to be shipped to your German address, the shipping company will request that you pay import taxes on the item (usually from 0% to 20% of the item’s value). Naturally, the shipping company does not know you are supposed to be exempt from these taxes, so there is some paperwork that is required to get your item delivered tax free. Once you have bought the item, you will have to go to the Customs office on GK (Building 84) with your receipt and request an AE Form 550-175A. The form is good for 90 days, so apply for the form early. This way, you can have it ready to go once the shipper contacts you about the import taxes.
How your form is processed by the shipper is different for each company so you will have to ask their employees about that part of the process. I know FedEx’s closest customs office is at the Frankfurt Airport and you must be present to clear customs, so tax free may or may not be worth your time.