I'm not sure the process is any different from here in the US. In general, you want to start the process about three months before you'd like to pick the car up in Munich. You place your order and give your dealer 3 desired pick-up dates. After a few weeks you receive confirmation of your pick-up date/time.
From there, your CA must formally submit your ED purchase order at least 4 weeks (I think) in advance of the delivery date including all of your pertinent info and a copy of your passport.
You visit the dealer one last time a week or so prior to delivery to execute the contract/lease.
There's a lot of waiting, but it's a pretty simple process. The trick is to start the process well in advance.