The vendor must issue you a MWSt return form:
http://www.zoll.de/e0_downloads/b0_v...cheinigung.pdf
which you need to get certified by German customs after you checked in for your flight outside the EU.

In MUC you need to checkin, tag your luggage to the final destination, show it to customs, get the required stamp on the required form, and then give your luggage to LH.
http://www.munich-airport.de/EN/Area...ew1/index.html
The german site is more detailed:
http://www.munich-airport.de/DE/Area...lug/index.html

The stamped form then needs to be returned to the original vendor, who will give you the cash back and claim the money back on his next VAT tax return. Some vendors wire you the money to a german bank account if you send the papers to them by mail.

The above is the correct way to get the 16/19% VAT back. German shops also have the global refund tax free check system, where you only get 10% back as the agency handles all the paperwork afterwards.
http://www.globalrefund.com/