This process goes up and down a hierarchical chain. At the lowest level, you have relatively junior personnel working out the nitty-gritty aspects of policy: who will do what, exactly, with what money, according to which laws. These recommendations are kicked up to higher levels, who might either approve them or send them back down to be revised, or to answer questions, or to consider more contingencies.
Eventually, though, something like a coherent set of options might make its way up to the principles committee—the actual NSC—who will then present those options to the president to either select one to approve or restart the whole process if he doesn’t like them.