I have a Jack Russell Terrier mix that will do this trick from the sit-up-pretty. It isn't hard to teach. First teach the dog the down command and then to lay over on the side at the "bang" command. Add a stay command and you have a "dead dog". You can start dropping the stay command once you teach the dog a release command such as "free dog". Most will learn faster if you use treats at each step in the very beginning. Most love to "perform" on command (especially if there's goodies involved) and most of the people I know that have seen Shiloh do her dead dog routine can't get over it and want to see it again and again. We'll do it a couple of times, but she gets tired of it and bored, so we stop before then.
We also taught this to our Cattle Dog mix and then often had to remind her that "dead dogs don't wag". It got to be part of the routine with her.