I’ve always been a little confused about this. If God is dead then somehow humans lose all their morals and any human actions are permitted, right?. This doesn’t quite make a whole lot of sense to me. Plenty of atheists still have morals? Aren’t morals innate?
"God is dead" does not imply that morality does not exist. It implies that there is no one universal transcendental morality. Rather there are many little moralities (just as for postmodernists there is no one grand narrative of history, there are many narratives that can exist side by side). Powerful and healthy people should invent their own morals. Also, morality is not set in stone, it can change, evolve or die.
According to Nietzsche, Christianity is an example of a morality that died, but people still have not caught up to the fact.
According to my understanding, the statement "God is dead." marks the death of authority-based, externally imposed morality as we see in religious domain. This brings on the field the need for another morality--now internally based--that comes from our heart. Otherwise we will loose all our moral compass and fall into hell of animal life of immorality.
This new internally based morality is totally subjective and cannot be measured by external behavior. To some degree it can but ultimately we are the whiteness of our actions and accusations that come from our heart (in case we commit an moral offense).